|
Tutors Answer Your Questions about Geometry proofs (FREE)
Question 175256: __ __
Given: CK is the perpendicular bisector of AE
Prove: triangle CAK is congruent to triangle CEK: __ __
Given: CK is the perpendicular bisector of AE
Prove: triangle CAK is congruent to triangle CEK
Answer by gonzo(563)  (Show Source):
You can put this solution on YOUR website!ck is the perpendicular bisector of ae (given).
this means that ac = ce (bisector of a line splits the line into 2 congruent parts)
this also means that angle ack equals angle eck = 90 degrees (perpendicular line creates 90 degree angle with the line it intersects)
kc congruent to kc (same line)
triangle akc congruent to triangle ekc (sas)
---
the words may not be exactly the way they would put them in your book but the concept is accurate.
the triangles are congruent by sas.
---
|
Question 175013: I am a 10th grade in geometry. Please help me with this proof.
Given: rhombus ABCD, line DEF, line ABF, and E is the midpoint of line DF.
I have to prove that line AD is congruent to line BF.
I marked the diagram marking drawing line DE congruent to line EF.
From this point I dont know where to start. Please help me. : I am a 10th grade in geometry. Please help me with this proof.
Given: rhombus ABCD, line DEF, line ABF, and E is the midpoint of line DF.
I have to prove that line AD is congruent to line BF.
I marked the diagram marking drawing line DE congruent to line EF.
From this point I dont know where to start. Please help me.
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!
*************************************************************************
statement reason
*************************************************************************
1. rhombus ABCD 1. Given
line DEF, line ABF
E is the midpoint of line DF
2. DE congruent to EF 2. definition of midpoint
3. DC congruent to AD 3. def. of rhombus
4. angle CDE congruent angle BFE 4. alternate interior angles
transversal to parallel line
ABF and DC
5. BEF congruent to DEC 5.opposite angles of intersecting
lines
6.tri BFE and tri CDE congruent 6. ASA
7. DC congruent BF 7. CPCTC
8. BF congruent AD 8. transitive prop (statements
3,7)
ASA- angle side angle
:
CPCTC congruent parts of congruent triangles are congruent
:
|
Question 174950: Hello, I am a 10th grade and I really need help with this proof please. The question is triangle ACB. At point C, two lines are drawn. Point D and E. Which go on the same line of A and B, so points D and E are in between those two corners/points. I was just describing it, thats not the question.
The Given: angle CDE is congruent to angle CED, line AD is congruent to line EB.
I need to prove that angle ACD is congruent to angle BCE.
So far I drew that angle CDE is congruent to angle CED. I marked the triangle. and that AD is congruent to EB. I dont know where to start. Please help me.
: Hello, I am a 10th grade and I really need help with this proof please. The question is triangle ACB. At point C, two lines are drawn. Point D and E. Which go on the same line of A and B, so points D and E are in between those two corners/points. I was just describing it, thats not the question.
The Given: angle CDE is congruent to angle CED, line AD is congruent to line EB.
I need to prove that angle ACD is congruent to angle BCE.
So far I drew that angle CDE is congruent to angle CED. I marked the triangle. and that AD is congruent to EB. I dont know where to start. Please help me.
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!
***************************************************************************
statement reason
***************************************************************************
1.angle CDE congruent to angle CED 1.Givens
AD congruent to EB
2.CDA + CDE = 180 2.Partition postulate
CEB + CED = 180
3.CDA+CDE = CEB+CED 3.transitive prop.
4.CDE+CDE = CEB+CDE 4.substition prop(CDE congruent CED)
5.CDE congruent CBE 5.subtraction prop.
6.CD congruent to CE 6.corresponding sides and angles of
isosceles triangle are congruent
7.tri ACD congruent tri BCE 7.SAS
8.ACD congruent BCE 8. CPCTC
partition post.-the whole is equal to the sum of the parts.
:
SAS- If two sides and the included angle of one triangle ar congruent
to the correspoinding parts of another triangle then triangles are congruent
:
CPCTC- Corresponding parts of congruent triangles are congruent
|
Question 174596: Hi I need help providing reasons for this proof.
I already provided some but don't know the rest.
Given: Square ABCD, Diagonals AC and BD
Prove:∠DEC and ∠BEC are right angles.
Statements: Reasons
scuare ABCD: Given.
segment DC is congruent to segment BC:
segment DE is congruent to segment BE:
segment EC is congruent to segment EC: Reflexive Property of Congruence.
triangle DEC is congruent to triangle BEC:
angle DEC is congruent to angle BEC:
measure of angle DEC is equal to measure of angle BEC: Definition of Congruence.
angle DEC supplements angle BEC:
measure of angle DEC plus measure of angle BEC equals 180degrees: Definition of supplementary angles.
measure of angle DEC equals measure of angle BEC queals 90degrees: Substitution and Division Property of Equality.
angle DEC and angle BEC are right angles: Definition of a right angle.: Hi I need help providing reasons for this proof.
I already provided some but don't know the rest.
Given: Square ABCD, Diagonals AC and BD
Prove:∠DEC and ∠BEC are right angles.
Statements: Reasons
scuare ABCD: Given.
segment DC is congruent to segment BC:
segment DE is congruent to segment BE:
segment EC is congruent to segment EC: Reflexive Property of Congruence.
triangle DEC is congruent to triangle BEC:
angle DEC is congruent to angle BEC:
measure of angle DEC is equal to measure of angle BEC: Definition of Congruence.
angle DEC supplements angle BEC:
measure of angle DEC plus measure of angle BEC equals 180degrees: Definition of supplementary angles.
measure of angle DEC equals measure of angle BEC queals 90degrees: Substitution and Division Property of Equality.
angle DEC and angle BEC are right angles: Definition of a right angle.
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!
***********************************************************************
statement reason
***********************************************************************
1.ABCD(square) 1.given
diagonals AC and BD
2.DC congruent to BC 2.def. of a square
DE congruent to BE diagonals bisect each other
3.EC congruent to EC 3. reflexive prop
4.tri DEC congruent tri BEC 4. SSS
5.angle DEC congruent to angle BEC 5. CPCTC
measure of angles congruent congruency def.
6.angle DEC + BEC = 180 6. linear pair
7.angle DEC= angle BEC equals 7. substitution prop.
90 degrees division prop.
8.angle DEC and BEC are right angles 8.def. of right angles
SSS-If three sides of one triangle are congruent to 3 sides of another triangle the triangles are congruent
:
CPCTC-corresponding parts of congruent triangles are congruent.
:
LINEAR PAIR: If two angles form a linear pair, they are supplementary.
|
Question 174585: My teacher assigned a problem called Dilcue's Chair. She said that it required some research to answer and I have tried to research the answer online all week and I have found nothing. The problem says that the chair was built such that the legs, segment HN and segment AO are attached at their midpoint R. Even though the legs turn out to be unequal in length, the seat of the chair, segment HA, is parallel to the floor, segment ON. Can you please help me solve this problem? Thank You. : My teacher assigned a problem called Dilcue's Chair. She said that it required some research to answer and I have tried to research the answer online all week and I have found nothing. The problem says that the chair was built such that the legs, segment HN and segment AO are attached at their midpoint R. Even though the legs turn out to be unequal in length, the seat of the chair, segment HA, is parallel to the floor, segment ON. Can you please help me solve this problem? Thank You.
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!Do you have any way to copy the picture of what you are looking at. Hard to picture what R is. If the HN and AO are the legs then the only midpoint of those segments would be a line between the two of them or a line that connects their midpoints and I dont see any reason why one leg cant be longer than the other it would just make at least one of the legs form an angle other than 90 degrees.
|
Question 173738: Hi, I am trying to solve a problem-- I have to write a paragraph proof for If m<1=m<2, then m <1=m<2. The diagram cannot be loaded onto this box forum and it is not in a book. sorry but maybe this is enough information to help you out? if not that is okay.: Hi, I am trying to solve a problem-- I have to write a paragraph proof for If m<1=m<2, then m <1=m<2. The diagram cannot be loaded onto this box forum and it is not in a book. sorry but maybe this is enough information to help you out? if not that is okay.
Answer by midwood_trail(310) (Show Source):
You can put this solution on YOUR website!Hi, I am trying to solve a problem-- I have to write a paragraph proof for If m<1=m<2, then m <1=m<2. The diagram cannot be loaded onto this box forum and it is not in a book. sorry but maybe this is enough information to help you out? if not that is okay.
====================
You need to write a paragraph proof concerning the measure of two angles but your question does not make sense as typed.
Notice that you said:
"I have to write a paragraph proof for If m<1 = m<2, then m <1 = m<2."
You repeated the fact that the measure of angle 1 = the measurte of angle 2 but no other information is given to establish a proof of any kind.
Check your question and write back when you have the entire given information about the angles at hand.
|
Question 173114: Given: Angle RBA is congruent to angle DAB; Angle D is congruent to angle R.
Prove: triangle DBX is congruent to triangle RAX: Given: Angle RBA is congruent to angle DAB; Angle D is congruent to angle R.
Prove: triangle DBX is congruent to triangle RAX
Answer by nycsub_teacher(80) (Show Source):
You can put this solution on YOUR website!Are you sure this is not a typo?
You said that angle RBA is congruent to angle DAB but these angles are not found in the given triangles that must be proven.
Angle B is part of triangle DBX and angle D is not in triangle RAX.
This creates a problem because both triangles share an angle that belongs the other.
I will let you reply.
If it is not a typo, then say so.
|
Question 173109This question is from textbook 
: Given: RS bisects
Prove: Triangle PQR is isoscelesThis question is from textbook
: Given: RS bisects
Prove: Triangle PQR is isosceles
Answer by nycsub_teacher(80) (Show Source): |
Question 174284: Given: ABCD is a square and XYZW is a figure inside the square
AX is congruent to BY which is congruent to CZ which is congruent to DW
BX is congruent to CY which is congruent to DZ which is congruent to AW
Prove that WXYZ is a square: Given: ABCD is a square and XYZW is a figure inside the square
AX is congruent to BY which is congruent to CZ which is congruent to DW
BX is congruent to CY which is congruent to DZ which is congruent to AW
Prove that WXYZ is a square
Answer by Edwin McCravy(2188) (Show Source):
You can put this solution on YOUR website!Given: ABCD is a square and XYZW is a figure inside the square
AX is congruent to BY which is congruent to CZ which is congruent to DW
BX is congruent to CY which is congruent to DZ which is congruent to AW
Prove that WXYZ is a square
I'll just outline the proof. You will have to write it
up as a two-column proof.
Now these four outer triangles shown below
are easily proved congruent by SSS:
Now by subtracting the sum of the measures of a
pair of congruent angles in each corner of the
big given square from 90° you get that these
four angles at A, B, C, and D, shown below are
all congruent:
Therefore the four triangles shown below around
the center quadrilateral are congruent by SAS:
Therfore the center figure WXYZ is at least a
rhombus, that is, all four sides are congruent,
by "corresponding parts of congruent triangles".
Now let's go back to the original figure:
Finally at each corner point of the inside figure,
X, Y, Z, and W, there are 4 adjacent angles which have
sum 360°. Three of the angles at each of those
corner points X,Y,Z, and W, are congruent to three
of the angles at each of the other corner point.
So by subtracting the measures of those three angles
from 360°, we get that each of the interior angles of the
the inner quadrilateral WXYZ have the same measure.
Now since the sum of the measures of the interior
angles of any quadrilateral is (4-2)×180° or 360°,
each of the corner points of the inside quadrilateral
must be 360°÷4 or 90°. Thus it is a rhombus with
four 90° interior angles, which is a square.
Edwin
|
Question 173843This question is from textbook geometry
: Write a paragraph proof.
Given: measure of angle GFI = measure of angle HFJ
Prove: measure of angle GFH = measure of angle HFIThis question is from textbook geometry
: Write a paragraph proof.
Given: measure of angle GFI = measure of angle HFJ
Prove: measure of angle GFH = measure of angle HFI
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!this is the vertical angle theorm. I am assuming in the prove part that you made a typo and that it should be GFH=JFI not GFH=HFI...I am writing this based on that assumption. If this is not correct you are somehow going to have to let us know what this picture looks like.
:
A straight line is 180 degrees making GJ a 180 degree angle. GFI+JFI=180 degrees and GFH+HFJ=180 degrees by the partition postulate which states that the whole is equal to the sum of the parts. GFI congruent to HFJ is given. HFJ+JFI=180 by substitution (GFI=HFJ)
HFJ+JFI=HFJ+GFH by transitive property. Therefore, JFI is congruent to GFH by the subtraction Postulate.
|
Question 173897This question is from textbook Geometry
: Can you please help me with the following problem <<<<< write a paragraph proof for theorem 6-6 >>>>> theorem 6-6 states that if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
THANK YOU!!!! :]This question is from textbook Geometry
: Can you please help me with the following problem <<<<< write a paragraph proof for theorem 6-6 >>>>> theorem 6-6 states that if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
THANK YOU!!!! :]
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!
.......................................................................
statement reason
1. angle Q congruent to angle S 1. Given
angle R congruent to angle T
2. angles Q+R+S+T =360 d 2.sum of the angles theorem
3. angles R+R+S+S= 360 d 3. subsitution post.
4. angles 2R+2S = 360 d 4. addition post.
5. angles R + S = 180 d 5. div. post.
6. angles T + S = 180 d 6. subst. post.
angles T + Q = 180 d
angles R + Q = 180 d
7. QRST is a parallelogram 7. if the consecutive angles of a quad
rilateral are supplementary the
quad is a parallelogram
|
Question 173426: Given: the measure of angle one equals the measure of angle 4
Prove: the measure of angle 2 equals the measure of angle 3
This book does not explain these problems so i can understand them. it has showed me how to do proofs but i still cannot understand what i am supposed to do.: Given: the measure of angle one equals the measure of angle 4
Prove: the measure of angle 2 equals the measure of angle 3
This book does not explain these problems so i can understand them. it has showed me how to do proofs but i still cannot understand what i am supposed to do.
Answer by solver91311(2163) (Show Source):
You can put this solution on YOUR website!Not having the diagram, there is no way to tell for certain, but I suspect that you need to demonstrate, either by use of the 5 postulates, or subsequent theorems already proven, that Angle 1 is equal in measure to either Angle 2 or Angle 3. Then show that Angle 4 is equal in measure to either Angle 3 or Angle 2. Then you can use the principle that things equal to equal things are themselves equal. If you know that a = b and c = d, then if you can demonstrate that b = c somehow, you know that a = d.
|
Question 173951: Given: Angle PQT and angle RQT are right angles, Line PQ is congruent to line QR, Angle VQT is congruent to angle SQT.
Prove: Line VQ is congruent to line SQ.: Given: Angle PQT and angle RQT are right angles, Line PQ is congruent to line QR, Angle VQT is congruent to angle SQT.
Prove: Line VQ is congruent to line SQ.
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!I hope I have drawn this figure correctly. I put the V between the P and P and the S between the R and T.
:
*********************************************************************
statement reason
*********************************************************************
1.Angle PQT and angle RQT are right angles 1.givens
PQ is congruent to line QR
2. QT congruent to QT 2. Reflexive prop.
3.Tri- PQT congruent to Tri RQT 3. SAS
4.angle RTQ congruent to angle PTQ 4. CPCTC
5.Tri SQT congruent to Tri VQT 5. ASA
6.angle VQT congruent SQT 6. given
7 VQ congruent to SQ 7. CPCTC
CPCTC- corresponding parts of congruent triangles are congruent
:
SAS,ASA- side angle side, angle side angle postulates
|
Question 173746This question is from textbook Geometry
: I need help with a proof. It is a pentagon with a star within it, the letters on the outside of the pentagon starting at the top and going righ are D, C, B, A and E. The only letter on the interior is an O in the bottom of a smaller pentagon formed by the star which is in the middle of the original. My goal is to make EC paralell to AB, please, please help if you can.This question is from textbook Geometry
: I need help with a proof. It is a pentagon with a star within it, the letters on the outside of the pentagon starting at the top and going righ are D, C, B, A and E. The only letter on the interior is an O in the bottom of a smaller pentagon formed by the star which is in the middle of the original. My goal is to make EC paralell to AB, please, please help if you can.
Answer by Edwin McCravy(2188) (Show Source):
You can put this solution on YOUR website!
1. The sum of the interior (n-2)*180° = (5-2)*180° =
angles is 540° 3*180° = 540°
2. ÐABC = 72° All interior angles of a regular
polygon are equal, and 540°÷5=72°
3. AB = BC All sides of a regular polygon
are equal.
4. DABC is isosceles Two sides equal, AB = BC
5. ÐBAC+ÐBCA+ÐABC=180° The sum of the interior angles
of a triangle is 180°
6. ÐBAC+ÐBCA+108°=180° Substituting 72° for ÐABC, since
they are equal.
7. ÐBAC+ÐBCA=72° Subtracting equals from equals,
(subtract 108° from both sides)
8. ÐBAC = ÐBCA Base angles of isoceles DABC
9. ÐBAC = ÐBCA = 36° Equal angles, each half of 72°, from 7
10. ÐCDE = 72° All interior angles of a regular
polygon are equal, and 540°÷5=72°
11. CD = DE All sides of a regular polygon
are equal.
12. DCDE is isosceles Two sides equal, CD = DE
13. ÐDCE+ÐDEC+ÐCDE=180° The sum of the interior angles
of a triangle is 180°
14. ÐDCE+ÐDEC+108°=180° Substituting 72° for ÐCDE, since
they are equal.
15. ÐDCE+ÐDEC=72° Subtracting equals from equals,
(subtract 108° from both sides)
16. ÐDCE = ÐDEC Base angles of isoceles triangle CDE
17. ÐDCE = ÐDEC = 36° Equal angles, each half of 72°, from 15.
18. ÐBCA = 36° From 9.
19. ÐDCE = 36° From 17.
20. ÐBCA+ÐACE+ÐDCE = ÐBCD Whole = sum of parts.
21. ÐBCD = 108° Reason 2
22. ÐBCA+ÐACE+ÐDCE = 108° Substituting equals for equals
23. 36° + ÐACE + 36° = 108° Subs. equals for equals, using
18 and 19.
24. 72° + ÐACE = 108° Adding 36°+36° in 22.
25. ÐACE = 36° Subtract equals from equals.
(Subtract 72° from both sides of 25.
26. ÐBAC = 36° Step 9
27. ÐACE = ÐBAC Both equal 36°
28. EC ú÷ AB Equal alternate interior angles ÐACE and
ÐBAC when transversal AC cuts lines
EC and AB
Edwin
|
Question 174240: can you help me with this please...Thank you
Given:ABCD is a rectangle E is the midpoint of line AD
Prove: traingle BEC is isosceles
please help... really appreciate it thank you: can you help me with this please...Thank you
Given:ABCD is a rectangle E is the midpoint of line AD
Prove: traingle BEC is isosceles
please help... really appreciate it thank you
Answer by vleith(1235) (Show Source):
You can put this solution on YOUR website!Draw the rectangle ABCD. Then add in point E. E is the midpoint of AD. So the length AE = ED.
Now draw in line segments BE and CE.
What you have now are a rectangle that is composed of 3 smaller triangles. The triangles are ABE, BEC and DEC.
You are asked to prove BEC is isosceles. That means you must prove BEC has two sides of equal length.
Look at triangles AEB and DEC. You know a rectangle has 4 90 degree angles in it. So the angles EAB and EDC are both 90.
You know the tow lengths AE and ED are equal.
You also know that opposite sides of a rectangle are eqaul in length. So AB = CD.
Side-angle-side is one way to prove two triangles are congruent. ABE and DEC have SAS congruence. Congruent triangles have all 3 sides equal. So BE = EC.
Thus BEC has two equal sides and must be, therefore, be isosceles
|
Question 173953: Given: line WJ is congruent to line kz, and w and angle k are right angles
prove: triangle jwz is congruent to triangle zkj
hint: 4 steps: Given: line WJ is congruent to line kz, and w and angle k are right angles
prove: triangle jwz is congruent to triangle zkj
hint: 4 steps
Answer by gonzo(563) (Show Source):
You can put this solution on YOUR website!from the information provided, it looks like these triangles are formed by taking a rectangle and drawing a diagonal from one corner to the other.
the rectangle would be JKZW going clockwise from J which is in the upper left corner of the rectangle.
the diagonal is JZ.
we given that WJ = ZK.
these are the two vertical lines on the left side and right side of this rectangle.
we are also given that angle W and angle K are right angles.
there may be a couple of ways of proving that triangle JWZ is congruent to triangle ZKJ, but one way is to use the hypotenuse leg theorem.
that theorem is:
any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
-----
the congruent legs are JW and KZ.
the congruent hypotenuse are JZ and JZ (the same diagonal applies to both triangles).
-----
|
Question 173749: Given: Segment AB is parallel to segment BE; Segment CD is parallel to segment BE; Segment AD is perpendicular to segment CE
Prove: Angle A is congruent to angle C
Here's a picture to help you:
http://i164.photobucket.com/albums/u27/foxymccloud/321gogeometry.jpg: Given: Segment AB is parallel to segment BE; Segment CD is parallel to segment BE; Segment AD is perpendicular to segment CE
Prove: Angle A is congruent to angle C
Here's a picture to help you:
http://i164.photobucket.com/albums/u27/foxymccloud/321gogeometry.jpg
Answer by Edwin McCravy(2188) (Show Source):
You can put this solution on YOUR website!Given: Segment AB is parallel to segment BE; Segment CD is parallel to segment BE; Segment AD is perpendicular to segment CE
Prove: Angle A is congruent to angle C
Sorry, but none of the things given are true. You've got the
lettering wrong, either in the problem or on the figure from
Photobucket. Please repost a corrected version and we can help
you.
Note: If you will copy and paste the following code, placing triple
open braces, three of these {, before it, and triple
close braces, three of these }, after it, you will get
the above figure:
drawing(400,228.6,-3,4,-1,3,
triangle(-2,0,0,0,-2,4/3),triangle(0,0,3,0,0,2),line(-3,0,4,0),
rectangle(-2,0,-1.8,.2), rectangle(0,0,.2,.2), locate(-2,0,B),
locate(0,0,D),locate(3,0,E),locate(-2,1.6,A),locate(0,2.26,C))
The key for open brace "{" is the key just right of the P, shifted.
The key for close brace "}" is the key just right of that, the "}",
also shifted.
Edwin
|
Question 174017: Given: RP is congruent to QS
RS is congruent to QP
Prove that: triangle RPQ is congruent to triangle QSR: Given: RP is congruent to QS
RS is congruent to QP
Prove that: triangle RPQ is congruent to triangle QSR
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!
*************************************************************************
statement reason
*************************************************************************
1. RP congruent to QS 1.given
RS congruent to QP
2. QR congruent to QR 2. reflexive property
3. tri RPQ congruent to tri QSR 3. SSS theorem
SSS theorem states that if three sides of one triangle are congrent to 3 sides of another triange then the triangles are congruent to one another
|
Question 173907This question is from textbook geometry integration applications connections
: can you please help me with this problem <<<< write a proof about of Theorem 6-6 >>>>> theorem 6-6 states that if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
THANK YOU SO MUCH!!
This question is from textbook geometry integration applications connections
: can you please help me with this problem <<<< write a proof about of Theorem 6-6 >>>>> theorem 6-6 states that if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
THANK YOU SO MUCH!!
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!
.......................................................................
statement reason
1. angle Q congruent to angle S 1. Given
angle R congruent to angle T
2. angles Q+R+S+T =360 d 2.sum of the angles theorem
3. angles R+R+S+S= 360 d 3. subsitution post.
4. angles 2R+2S = 360 d 4. addition post.
5. angles R + S = 180 d 5. div. post.
6. angles T + S = 180 d 6. subst. post.
angles T + Q = 180 d
angles R + Q = 180 d
7. QRST is a parallelogram 7. if the consecutive angles of a quad
rilateral are supplementary the
quad is a parallelogram
|
Question 173906: Hi! How Are You?! im having trouble with this proof can u please help me?!
Rhombus ABCD
Given
Line AB is parallel to line CD
Line AB is congruent to line CD
Line AC is perpendicular to BD
Prove:
ABCD is a Rhombus
i dont get it so please help me thank you.. : Hi! How Are You?! im having trouble with this proof can u please help me?!
Rhombus ABCD
Given
Line AB is parallel to line CD
Line AB is congruent to line CD
Line AC is perpendicular to BD
Prove:
ABCD is a Rhombus
i dont get it so please help me thank you..
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!
.............................................................................
Statement Reason
1. AB is parallel CD 1. Given
AB is congruent to CD
AC is perpendicular to BD
2. angle CDB congruent to angle ABD 2. BD transversal-Alt interior
angles.
3. BD congruent BD 3. reflexive prop
4. tri BCD is congruent to tri BAD 4. SAS
5. AD congruent BC 5. CPCTC
6. angle ABD congruent angle CBD 6. CPCTC
angle CDB congruent angle BDA
7. angle CBD congruent angle BDA 7. transitive prop S #2,6
8. BC is parallel to AD 8. alternate interior angles converse
9. ABCD is a paralleogram 9. def of parallelogram S #1,8
10.ABCD is a Rhombus 10 def of a rhombus S #1,5,9
SAS side angle side theorem
CPCTC- corresponding parts of congruent triangles are congruent
|
Question 173910:
Hi! How Are You?! im having trouble with this proof
can u please help me?!
D__________C
|\-------2/| I think u kinda get the figure?!? thers a rectangle
|-\------/-| With the diagonal inside and E is the midpoint of the
|-----E----| Diagonals
|-/------\-|
|/1_______\|
A B
Given
Line DB Bisects Line AC
(THey meet at point e in the middle of the rectangle)
Angle 1 is congruent to Angle 2
Prove ABCD = rectangle
Thank you for helping appreciate it! :
Hi! How Are You?! im having trouble with this proof
can u please help me?!
D__________C
|\-------2/| I think u kinda get the figure?!? thers a rectangle
|-\------/-| With the diagonal inside and E is the midpoint of the
|-----E----| Diagonals
|-/------\-|
|/1_______\|
A B
Given
Line DB Bisects Line AC
(THey meet at point e in the middle of the rectangle)
Angle 1 is congruent to Angle 2
Prove ABCD = rectangle
Thank you for helping appreciate it!
Answer by Edwin McCravy(2188) (Show Source):
You can put this solution on YOUR website!Given
Line DB Bisects Line AC (THey meet at point e in the middle of the rectangle)
Angle 1 is congruent to Angle 2
Prove ABCD = rectangle
That isn't necessarily true because ABCD could be only a
parallelogram, and not necessarily a rectangle, as you can
see from the drawing below, where the same things are given:
If there is something given that you omitted, then post again.
Edwin
|
Question 173911: Hi! How Are You?! im having trouble with this proof can u please help me?!
D_________C I hope you ge tthe idea how it is... Can u please check if
|\------/| it is right.. and if its wrong can u please give me the
|-\----/-| corrections
|--\--/--|
|___\/___|
A---M----B
Given:
ABCD is a rectangle
M is the midpoint of line AB
Prove:
line DM is congruent to Line CM
i wrote
1. ABCD is a rectangle - Given
2. Line DA + Line CB is Congruent - Properties of a rectangle
Angle DAM + Angle CBM is Congruent -
3. M is the midpoint of Line AB - Given
4. Line AM + Line BM is congruent - DEFfinition of a midpoint
5. Triangle DAM + Triangle CBM - S.A.S
6. Line DM is congruent to Line CM - CPCTC
: Hi! How Are You?! im having trouble with this proof can u please help me?!
D_________C I hope you ge tthe idea how it is... Can u please check if
|\------/| it is right.. and if its wrong can u please give me the
|-\----/-| corrections
|--\--/--|
|___\/___|
A---M----B
Given:
ABCD is a rectangle
M is the midpoint of line AB
Prove:
line DM is congruent to Line CM
i wrote
1. ABCD is a rectangle - Given
2. Line DA + Line CB is Congruent - Properties of a rectangle
Angle DAM + Angle CBM is Congruent -
3. M is the midpoint of Line AB - Given
4. Line AM + Line BM is congruent - DEFfinition of a midpoint
5. Triangle DAM + Triangle CBM - S.A.S
6. Line DM is congruent to Line CM - CPCTC
Answer by solver91311(2163) (Show Source):
You can put this solution on YOUR website!You need to give a reason for Angle DAM congruent to Angle CBM (Properties of a Rectangle)
I presume CPCTC means something having to do with corresponding parts of congruent triangles are congruent.
Given that, you have this spot on.
|
Question 173896: what is a two-column proof on Theorem 6-6?: what is a two-column proof on Theorem 6-6?
Answer by solver91311(2163) (Show Source): |
Question 173567This question is from textbook Integrated mathmatics
: RS bisects PQ at T. PQ bisects RS at T.
prove: Triangle PTS congruent Triangle QTRThis question is from textbook Integrated mathmatics
: RS bisects PQ at T. PQ bisects RS at T.
prove: Triangle PTS congruent Triangle QTR
Answer by nycsub_teacher(80) (Show Source):
You can put this solution on YOUR website!RS bisects PQ at T. PQ bisects RS at T.
prove: Triangle PTS congruent Triangle QTR
Statements..............................Reasons
(1) RS bisects PQ at T.................(1) Given
(2) PQ bisects RS at T.................(2) Given
(3) angle PST ≅ angle QRT........(3) supplements of congruent angles
(4) TS ≅ TR......................(4) Converse of Base Angles Theorem
(5) angle PTS ≅ angle QTR.........(5) Subtraction Property of Equality
(6) Triangle PTS ≅ Triangle QTR...(6) Angle side angle
|
Question 173835: Hello,
I have submitted the following (please open web link for my work)twice for grading, and my grader keeps telling me this:
"Through a point outside a line, there is exactly one line parallel to the given line." but this is Euclid's postulate and as such does not require proof. Please provide the theorem that can be proved in Euclidean geometry but not in non-Euclidean geometry."
http://www.taskstream.com/ts/brechtel/MGA5Task2.html-Web link for my work
Thanks for your help!: Hello,
I have submitted the following (please open web link for my work)twice for grading, and my grader keeps telling me this:
"Through a point outside a line, there is exactly one line parallel to the given line." but this is Euclid's postulate and as such does not require proof. Please provide the theorem that can be proved in Euclidean geometry but not in non-Euclidean geometry."
http://www.taskstream.com/ts/brechtel/MGA5Task2.html-Web link for my work
Thanks for your help!
Answer by solver91311(2163) (Show Source):
You can put this solution on YOUR website!Euclid's fifth postulate is "If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough." This postulate is equivalent to what is known as the parallel postulate, which is the statement you call a theorem. In fact, no one has ever been able to prove the fifth or the parallel postulates using the first four postulates. So your choice of a thing to show as a theorem that cannot be proven in Non-Euclidian Geometry was inappropriate. What you need to do is find a Theorem whose proof is based upon the fifth or parallel postulate, and show that the Theorem cannot be proven in an elliptic or hyperbolic geometry. I suggest you start looking in Euclid's Elements at Proposition 29.
Good luck.
|
Question 173520This question is from textbook geometry
: the lengths of the sides of a triangle are 2x+5, 3x+10, and x+12. Find the values of x that make the triangle isoceles.This question is from textbook geometry
: the lengths of the sides of a triangle are 2x+5, 3x+10, and x+12. Find the values of x that make the triangle isoceles.
Answer by checkley77(3848) (Show Source):
You can put this solution on YOUR website!2x+5=3x+10
-x=5
x=-5 not the 2 equal sides.
2x+5=x=12
x=12-5
x=7 equal sides when x=7.
3x+10=x+12
3x-x=12-10
2x=2
x=1 equal sides when x=1.
|
Question 173264: Given: H is the midpoint of segment DK and segment PG.
Prove: Segment DG is congruent to segment KP: Given: H is the midpoint of segment DK and segment PG.
Prove: Segment DG is congruent to segment KP
Answer by gonzo(563) (Show Source):
You can put this solution on YOUR website!angle DHG is congruent to angle KHP because opposite angles of intersecting lines are congruent (the two intersecting lines are DK and PG with the intersection point at H).
DH is congruent to HK because midpoint of a line segment creates two equal line segments.
GH is congruent to HP because midpoint of a line segment creates two equal line segments.
triangle DHG is congruent to triangle KHP by SAS (side angle side) postulate.
DG is congruent to PK because corresponding parts of congruent triangles are congruent.
|
Question 173232: i need help with this proof
given:line segment vt bisects line segment rw
line segment rw bisects line segment tv
prove:triangle rsv is equal and congruent to triangle tsw: i need help with this proof
given:line segment vt bisects line segment rw
line segment rw bisects line segment tv
prove:triangle rsv is equal and congruent to triangle tsw
Answer by colliefan(31) (Show Source):
You can put this solution on YOUR website!I take it that point S is the intersection of the 2 segments. If that is true,
RS is congruent to SW because VT bisects at S
VS is congruent to ST because RW bisects at S
angle rsv is congruent to angle WST because they are opposite angles
The triangles are congruent by SAS
|
Question 173265: Given: Segment CS and segment AT are altitudes; Segment CS is congruent to segment AT
Prove: Segment AS is congruent to segment CT
Use this diagram to help you:
http://i164.photobucket.com/albums/u27/foxymccloud/geometry.jpg: Given: Segment CS and segment AT are altitudes; Segment CS is congruent to segment AT
Prove: Segment AS is congruent to segment CT
Use this diagram to help you:
http://i164.photobucket.com/albums/u27/foxymccloud/geometry.jpg
Answer by jim_thompson5910(9869) (Show Source):
You can put this solution on YOUR website!
Statement Reason
-----------------------------------------------------------------------
1. Angle ASC is right angle Definition of Altitude (given)
2. Angle ATC is right angle Definition of Altitude (given)
3. Angle ATC = Angle ASC Right Angle Theorem
4. CS = AT Given
5. AC = AC Reflexive Property of Congruence
6. triangle ASC = triangle ATC SAS Postulate
7. AS = CT CPCTC
Notes:
# 1 Remember, an altitude is a segment that runs from one vertex to the opposite side (and forms a 90 degree angle with the opposite side).
# 2 The Right Angle Theorem states that all right angles are congruent.
# 3 CPCTC = Corresponding parts of congruent triangles are congruent.
|
Question 173153: ABC isosceles and CD is angle bisector of the vertex angle
prove that BD = AD
Thanks for your help: ABC isosceles and CD is angle bisector of the vertex angle
prove that BD = AD
Thanks for your help
Answer by jim_thompson5910(9869) (Show Source):
You can put this solution on YOUR website!If you draw the triangle, you might get this:
Since the triangle is isosceles, this means that AC and BC are congruent (since an isosceles triangle has equal sides). So this is given.
In order to prove that BD = AD, we need to show that the two triangles (that form when the segment CD is drawn) are congruent. Once we've proven that the two triangles are congruent, we can easily show that the corresponding parts are congruent.
Statement | Reason
------------------------------------------------------------------------
1. AC = BC Given
2. CD = CD Reflexive Property of Congruence
3. angle ACD = angle BCD Definition of Angle Bisector
4. triangle ACD = triangle BCD SAS Postulate
5. BD = AD CPCTC
Notes
#1) Remember an "angle bisector" cuts an angle in half. So this means that the two halves of the angle are equal (in this case angles ACD and BCD )
#2) statement 4 uses statements 1, 2, and 3.
#3) CPCTC stands for "Corresponding parts of congruent triangles are congruent".
|
Question 172823This question is from textbook Prentice hall mathematics Geometry
: I have this problem that i have to solve in front of my class tomorrow and my teacher did not tell if it was right or wrong...
It is a quadrilateral with 2 right trianglea at the 2 opposite corners of the quadrilateral both of their legs are congruent and there is 2 other triangles in the quadrilateral that are connected to both of the right triangles. its really confusing.
given: BE PERPENDICULAR TO AC, DF PERPENDICULAR TO AC
BE CONGRUENT TO DF, AF CONGRUENT TO EC
PROVE: AB CONGRUENT TO DCThis question is from textbook Prentice hall mathematics Geometry
: I have this problem that i have to solve in front of my class tomorrow and my teacher did not tell if it was right or wrong...
It is a quadrilateral with 2 right trianglea at the 2 opposite corners of the quadrilateral both of their legs are congruent and there is 2 other triangles in the quadrilateral that are connected to both of the right triangles. its really confusing.
given: BE PERPENDICULAR TO AC, DF PERPENDICULAR TO AC
BE CONGRUENT TO DF, AF CONGRUENT TO EC
PROVE: AB CONGRUENT TO DC
Answer by jim_thompson5910(9869) (Show Source): |
Question 172857: given Y is the midpoint of segment XZ, segment XV is congruent to segment ZW,segment XV is parallel to segment ZW prove triangle XVY is congruent to triangle ZWY: given Y is the midpoint of segment XZ, segment XV is congruent to segment ZW,segment XV is parallel to segment ZW prove triangle XVY is congruent to triangle ZWY
Answer by colliefan(31) (Show Source):
You can put this solution on YOUR website!Angles VXY and WZY are congruent because they are alternate interior angles.
XY is congruent to ZY because of the bisection
XV is congruent to segment ZW by the conditions of the problem
The triangles are congruent by SAS
|
Question 172860This question is from textbook GEOMETRY
: Given: BD is perpendicular to AC and BD bisects AC
Prove: Angle ABD and angle BCD are complementary anglesThis question is from textbook GEOMETRY
: Given: BD is perpendicular to AC and BD bisects AC
Prove: Angle ABD and angle BCD are complementary angles
Answer by colliefan(31) (Show Source):
You can put this solution on YOUR website!AD is congruent to DC because BD bisects AC
BD is a shared side of triangles BDA and BDC
angles ADB and CDB are both right angles and so are congruent
Triangles ADB and CDB are congruent by SAS
Angles CBD and ABD are congruent because these triangles are congruent
Angles CBD and BCD are conplementary because they are the acute angles in a right triangle
Angle ABD is then complementary to BCD because ABD and CBD are congruent
|
Question 172674This question is from textbook GEOMETRY
: how do you solve this? i've looked at it for maybe, 1 hour, and i cannot solve.
thanksThis question is from textbook GEOMETRY
: how do you solve this? i've looked at it for maybe, 1 hour, and i cannot solve.
thanks
Answer by Alan3354(1916) (Show Source): |
Question 172105: I don't know exaclty how to do proofs. what should I do?: I don't know exaclty how to do proofs. what should I do?
Answer by Alan3354(1916) (Show Source): |
Question 171690: what does reflexive mean, can i get an example?: what does reflexive mean, can i get an example?
Answer by jim_thompson5910(9869) (Show Source): |
Question 171290This question is from textbook Geometry Concepts and Skills
: if line ab is congruent to line ae and angle acb is congruent to angle ade angle b is congruent to angle eThis question is from textbook Geometry Concepts and Skills
: if line ab is congruent to line ae and angle acb is congruent to angle ade angle b is congruent to angle e
Answer by Mathtut(1267) (Show Source):
You can put this solution on YOUR website!no not necessarily you can make two 90 degree angles with acb and ade and get very different angles for b and e. In the drawing below you can see that AB and AE are congruent and ACB congrent to ADE both at 90 degrees. but angle B and E are clearly not congruent
|
Question 171263This question is from textbook Geometry
: I have tried many approaches. Still i cant find the answer. Your help is greatly appreciated.
THANK YOUThis question is from textbook Geometry
: I have tried many approaches. Still i cant find the answer. Your help is greatly appreciated.
THANK YOU
Answer by Mathtut(1267) (Show Source): |
|
|
| |