Questions on Geometry: Proofs in Geometry answered by real tutors!

Tutors Answer Your Questions about Geometry proofs (FREE)

Question 1210360: A quadrilateral, STVR has an exterior angle VRX. Given angle XRV is congruent to angle RST, and angle RSV is congruent to angle TVS, prove that RSTV is a parallelogram.
Click here to see answer by Edwin McCravy(20056)

Question 1168329: Write an indirect proof to prove Theorem 4-2: If there is a line and a point not on the line, then exactly one plane contains them.
Click here to see answer by CPhill(1959)

Question 1168388: A cat has thirteen kittens. Eight of the kittens have white hair, six of the kittens have spots, and eight of the kittens have long tails. All of the kittens have at least one of these traits. One kitten is white with spots and a long tail. Three of the kittens are white with spots. Two kittens have spots and long tails. One kitten has white hair but does not have spots or a long tail.
A. Draw a Venn diagram for this problem.
B. How many kittens are white with long tails, but don't have spots?
Thank you

Click here to see answer by CPhill(1959)

Question 1166437: Prove the “ruler ﬂipping lemma”: if f : l → R is a coordinate function for a line l, then the function f0, deﬁned, for every point P ∈ l, by f0(P) = −f(P), is also a coordinate function for l.

Click here to see answer by ikleyn(52788)

Question 1167304: FP intersects XS at 0. Prove <1 and <2 are vertical angles. 
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Question 1169211: Given that ∠FAB≅∠GED and C is the midpoint of AE¯¯¯¯¯, which of the following proves that △ABC≅△EDC?
https://thinkwell.cachefly.net/questionbank/95001-96000/95608/img/95608a.svg
A.
1. ∠FAB≅∠GED (Given)2. ∠BAC is the supp. of ∠FAB; ∠DEC is thesupp. of ∠GED (Def. of Supp. ∠s)3. ∠BAC≅∠DEC (≅ Supp. Thm.)4. ∠ACB≅∠DCE (Vert. ∠s Thm.)5. C is the midpoint of AE¯¯¯¯¯ (Given)6. AC¯¯¯¯¯≅EC¯¯¯¯¯ (Def. of mdpt.)7. △ABC≅△EDC (by ASA Steps 3, 6, 4)

B.
1. ∠FAB≅∠GED (Given)2. ∠BAC is the supp. of ∠FAB; ∠DEC is thesupp. of ∠GED (Def. of Supp. ∠s)3. ∠BAC≅∠DEC (≅ Supp. Thm.)4. ∠ACB≅∠DCE (Adj. ∠s Thm.)5. C is the midpoint of AE¯¯¯¯¯ (Given)6. AC¯¯¯¯¯≅EC¯¯¯¯¯ (Def. of mdpt.)7. △ABC≅△EDC (by ASA Steps 3, 6, 4)

C.
1. ∠FAB≅∠GED (Given)2. ∠BAC is the supp. of ∠FAB; ∠DEC is thesupp. of ∠DEG (Def. of Supp. ∠s)3. BC¯¯¯¯¯≅CD¯¯¯¯¯ (≅ Supp. Thm.)4. ∠ACB≅∠BCE (Vert. ∠s Thm.)5. C is the midpoint of AE¯¯¯¯¯ (Given)6. BC¯¯¯¯¯≅CD¯¯¯¯¯ (Def. of mdpt.)7. △ABC≅△EDC (by SAS Steps 3, 1, 6)

D.
1. ∠FAB≅∠GED (Given)2. ∠BAC is the supp. of ∠FAB; ∠DEC is thesupp. of ∠GED (Def. of Supp. ∠s)3. BC¯¯¯¯¯≅CD¯¯¯¯¯ (≅ Supp. Thm.)4. ∠ACB≅∠BCE (Vert. ∠s Thm.)5. C is the midpoint of AE¯¯¯¯¯ (Given)6. BC¯¯¯¯¯≅CD¯¯¯¯¯ (Def. of mdpt.)7. △ABC≅△EDC (by SAS Steps 3, 1, 6)

Click here to see answer by CPhill(1959)

Question 1170173: I have two right triangles that are connected at point x. On the right, there is triangle one which has point v at the top, w at the corner, and x which connects to triangle two which has point z at the bottom, connected to y which connects to x.
I am given that line WV is perpendicular to line WY. I am also given that line ZY is perpendicular to line WY, as well as line WV is congruent to ZY. I am supposed to prove that the triangles are congruent and X is the midpoint of line VZ.
I do have a 4th statement that I attempted to do. That is that angle W is congruent to angle Y because of the def. of perpendicularity. I also have about half of the fifth statement which is that angle 1 and angle 2 are congruent. I don't know how to prove this with reason. I need help.
Click here to see answer by CPhill(1959)

Question 1170429: Given: \overline{CA}
CA
bisects \angle BAD∠BAD and \angle B \cong \angle D.∠B≅∠D.
Prove: \triangle ABC \cong \triangle ADC△ABC≅△ADC.
Click here to see answer by CPhill(1959)

Question 1168400: X is the midpoint of WY, X is the midpoint of XZ, VZ ≈WY, Prove VX ≈ WX
Click here to see answer by ikleyn(52788)

Question 1173654: Provide a two column proof or paragraph proof.
Given MA and AI are perpendicular: RS and AI are perpendicular : K is the midpoint of MT.
Prove: Triangles MAK and TIK are congruent. (If didn't work prove Triangles MKI and TKA are congruent)
Click here to see answer by CPhill(1959)

Question 1175420: Suppose and are two non-intersecting chords of a circle. Take any point on the
arc not containing , . Let and intersect at , respectively. Show
that AQ×RB/QR
is constant (irrespective of position of ).
Click here to see answer by CPhill(1959)

Question 1177132: given: triangle abc is scalene
altitudes ae,cd
prove: ae is not congruent to cd

Click here to see answer by ikleyn(52788)

Question 1177132: given: triangle abc is scalene
altitudes ae,cd
prove: ae is not congruent to cd

Click here to see answer by CPhill(1959)

Question 1177180: Given: Segment NK is a median of triangle JMN; IN>NM Prove: m<1>m<2
Click here to see answer by CPhill(1959)

Question 1179586: https://ibb.co/jgpq3pX (Please copy paste the link to view the figure)
Given: AE = DE; EB = EC
Prove: a. Triangle AEB = Triangle DEC
b. Triangle ABC = Triangle DCB
Click here to see answer by CPhill(1959)

Question 1179587: https://ibb.co/M6MBW92
(please copy paste the link to view the figure)
Given: AB||CD; BE = DF; AE and CF are perpendicular to DB.
Prove: AD||BC
Click here to see answer by CPhill(1959)

Question 1182026: A student tried to trisect an angle G using the following procedure:
1. Mark off GA congruent to GB.
2. Draw AB
3. Divide AB into 3 congruent parts so that AX=XY=YB.
4. Draw GX and GY.
Show that the student did not trisect angle G (Hint: Show that GA>GY. Then use indirect proof to show that angle XGY is not equal to angle XGA.)
I know how to show that GA>GY (by SAS Inequality) but cannot show why angle XGY is not equal to angle XGA using indirect proof. I appreciate any help! Thanks in advance!
Click here to see answer by Edwin McCravy(20056)

Question 1181982: Given: angle QPS is equal and congruent to angle TPR
Prove: angle QPR is equal and congruent to angle TPS.
The diagram has angle QPT divided into 3 smaller angles.
Left: QPR
Interior: RPS
Right: SPT
The interior angle RPS is significantly larger than the 2 exterior angles QPR and SPT.

1.angle QPS =& congruent angle TPR. Given
2.m angle QPS = m angle TPR. Definition. of congruence
3.m angle QPS = m angle QPR + m angle RPS. Angle addition
m angle TPR = m angle TPS + m angle RPS. postulate
4. ____________________________. Substitution
5._______________________________. ________________
6. Angle QPR =&congruent to angle TPS. __________________
Click here to see answer by CPhill(1959)

Question 1182025: A student tried to trisect an angle G using the following procedure:
1. Mark off GA congruent to GB.
2. Draw AB
3. Divide AB into 3 congruent parts so that AX=XY=YB.
4. Draw GX and GY.
Show that the student did not trisect angle G (Hint: Show that GA>GY. Then use indirect proof to show that m I know how to show that GA>GY (by SAS Inequality) but cannot show why m
Click here to see answer by CPhill(1959)

Question 1182497: Consider two points A and B, whose position vectors are a and b. The angle bisector of AOB meets AB at X. Let vector OX = u(a+b). Similarly, let vector AX = d(AB),where . Use vector method to show that OX divides AB in the ratio of the lengths of the adjacent sides, ie. AX:XB = OA:OB

Click here to see answer by CPhill(1959)

Question 1185564: paragraph proof given angle A is congruent to angle D, O is the midpoint of line AD prove triangle AOB is congruent to triangle DOC answer
Click here to see answer by ikleyn(52788)

Question 1185390: 3. The coordinates of vertex A of the triangle ABC are (7, -4). If the coordinates of the centroid of the triangle are (1, 2), find the coordinates of the midpoint of the side BC.
Click here to see answer by greenestamps(13200)

Question 1191529: Draw a triangle with vertices A(0, 4), B(2, -2), and C(-2, -2). Apply a dilation centered at the origin with scale factor to this triangle and draw the resulting triangle,A'B'C'. In complete sentences, describe the following:
The relationship between corresponding sides in terms of their lengths.
The relationship between corresponding sides in terms of their orientations.
The relationship between corresponding angles in terms of their measures.

Click here to see answer by CPhill(1959)

Question 1191473: In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle RST is congruent to triangle RSQ given that RS ⊥ ST, RS ⊥ SQ, and ∠STR ≅ ∠SQR. Submit the entire proof to your instructor.
Given:
RS ⊥ ST
RS ⊥ SQ
∠STR ≅ ∠SQR
Prove:
△RST ≅ △RSQ

STATEMENT REASON
1.RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR 1.
2. 2.
3. 3.
4. △RST ≅ △RSQ 4.

Click here to see answer by CPhill(1959)

Question 1192419: Prove that if two intersecting line segments meet at their midpoints, the line
segments joining their endpoints are congruent.
Given: O is the midpoint of XY and of AB
Prove: XA ≅ BY

Click here to see answer by Edwin McCravy(20056)

Question 1209431: Given: Quadrilateral ABCD
Segment AC bisects angle DAB
Segment DB bisects angle ADC
Segment AB is parallel to segment DC
Prove: ABCD is a rhombus
Click here to see answer by math_tutor2020(3817)

Question 1208365: Given: Triangle ABC, Bisectors of < a and < b meet at O. Prove: m (< aob) > 90 degrees
Click here to see answer by greenestamps(13200)

Question 1208294: 1. If A, B, C, D are collinear and AB = 8, AC = 12, AD = 16, BC = 20,
BD = 24, CD = 28, find all possible betweenness relations.
2.Show that if A ∗ B ∗ C and B ∗ C ∗ D, then A ∗ B ∗ D and A ∗ C ∗ D.
[5]
Click here to see answer by ikleyn(52788)

Question 1208225: AB, DE and CF
AB||DE
CG bisects BCF
FG bisecs CFE
Prove
Click here to see answer by ikleyn(52788)

Question 1208064: Quadrilateral PQRS is cyclic and side PS = u is a
diameter of the circle. If PQ = QR = v, RS = w, and u, v,
and w are integers such that v does not equal w, prove that u cannot be a
prime number.
Click here to see answer by ikleyn(52788)

Question 1192638: Write the missing statement and reasons to complete the proof.
Given: 𝑁𝑂 ∥ 𝑀𝑃, ∠𝑁 ≅ ∠𝑃
Prove: 𝑀𝑁 ∥ 𝑂𝑃
( square with N on top left and O on top right, then M on bottom left and P on bottom right ) With a dash line going from M to O
Click here to see answer by mananth(16946)

Question 1179588: https://ibb.co/vwTrxgh
(Please copy paste the link to view the figure)
Given: JA = JL; JC bisects Angle AJL
Prove: KC bisects Angle AKL
Thank you :)
Click here to see answer by mananth(16946)

Question 1206239: Given:
RS ⊥ ST
RS ⊥ SQ
∠STR ≅ ∠SQR
Prove:
△RST ≅ △RSQ

STATEMENT REASON
1.RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR 1.
2. 2.
3. 3.
4. △RST ≅ △RSQ 4.

Click here to see answer by MathLover1(20850)

Question 1206186: Look at the figure below:
Triangle EFD has the measure of angle EFD equal to 60 degrees. G is a point on side DF. Points E and G are joined by a straight
https://api.agilixbuzz.com/Resz/~0.Bv8W_aJ6tRosNuyK.A.WQX-LKs4_7CtNbGXeaKp1TM-Q57bSJTC4440BKyZad8/196638831,F41,1,15,0,30,0,3/Assets/94559_55a90aae/image0044e8cadde.jpg
Make a two-column proof showing statements and reasons to prove that triangle DEF is similar to triangle DGE.
Click here to see answer by mccravyedwin(407)

Question 1206184: In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between segment AG and segment BF , while point E is the point of intersection between segment DG and segment BF.
https://api.agilixbuzz.com/Resz/~0.Bv8W_aJ6tRosNuyK.A.WQX-LKs4_7CtNbGXeaKp1TM-Q57bSJTC4440BKyZad8/196638831,F41,1,15,0,30,0,3/Assets/94559_55a90aae/05_08_1b.gif
The figure shows a polygon comprised of three triangles, ABC, CEG, and DFE.
Prove ΔABC ∼ ΔGEC.
Click here to see answer by MathLover1(20850)

Question 1206126: Prove by contradiction that the diagonals of a kite intersect at right angles? My proof is very wordy,can you help me be more precise. Thank you
Click here to see answer by math_tutor2020(3817)

Question 1206134: Prove 𝐶−𝐷=𝐶∩𝐷'. Just having a little bit of trouble with my wording of the proof. Thank you.
Click here to see answer by ikleyn(52788)

Question 1206128: Write a coordinate proof to show that the segments connecting the midpoints of any quadrilateral form a parallelogram. I think it is simpler to use vectors but not sure if I have to use midpoint formulas. Thank you.
Click here to see answer by greenestamps(13200)

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