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

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 Geometry: Proofs in Geometry Solvers Lessons Answers archive Quiz In Depth

 Question 28554: Gidday I have been asked to prove the following identity, and i have absolutely no idea what is being asked for. cos^2theta - sin^2theta = 1 - 2(sin^2theta) Thanks Darryl Click here to see answer by longjonsilver(2297)
 Question 28554: Gidday I have been asked to prove the following identity, and i have absolutely no idea what is being asked for. cos^2theta - sin^2theta = 1 - 2(sin^2theta) Thanks Darryl Click here to see answer by Paul(988)

 Question 29064: There is a rectangular box that has two right triangles in it. It is given that segmant AB is congruent to segmant CD, and segmant AB is perpendicular to segmant CD. I need to prove that triangle ABC is congruent to triangle CDA. Click here to see answer by venugopalramana(3286)

 Question 29579: Hello, Geometry tutor. Please help me with Problem #1: All of this is given: if triangle CDO is congruent to triangle CBO, then line segment DC is congruent to line segment BC by cpctc (corresponding parts of congruent triangles are congruent). Did I approach this problem correctly? I'm not sure about step 3 and step 4. I wrote my STATEMENTS and REASONS as follows: STATEMENT: 1. Line segment AC bisects line segment DB at point O. REASON: 1. Given. STATEMENT: 2. Line segments DO and BO are congruent. REASON: 2. Given. Definition of Bisector of a Segment. (by Definition 1.16 - A line that divides a line segment into two congruent line segments). STATEMENT: 3. Line segment AC is perpendicular to line segment BD. REASON: 3. Given. STATEMENT: 4. Angle 1 & 2 are adjacent angle's whose non-common side form a line. REASON: 4. Given. Definition of Perpendicular Lines. (by Definition 1.18 - Two lines are perpendicular if, & only if, they meet & form congruent adjacent angles). STATEMENT: 5. Line segment CO is congruent to line segment CO. REASON: 5. Given. Reflexive Law of congruent. (by Postulate 1.6 - states that any quantity is equal to itself). STATEMENT: 6. Triangle CDO is congruent to triangle CBO. REASON: 6. SAS is congruent to SAS. STATEMENT: 7. Line segment DC is congruent to line segment BC. REASON: 7. cpctc. (corresponding parts of congruent triangles are congruent). Click here to see answer by ikdeep(226)

 Question 31177: Hello! I need your help on the following proof: Given: measurement of angle 1 equals the measure of angle 3 Prove:measure of angle 4 plus measure of angle 2 equals 180 degrees. / \ / \ / 3 1 \2 <--------------------> 4/ / / I tried to recreate the diagram. I think 3 and 1 are interior angles.Thank you. Click here to see answer by troyapplehelen(46)

 Question 31170: Hello! I've been asked by my teacher to solve the following proof: Prove: If two parallel lines are cut by a transversal, then bisectors of corresponding angles are parallel. I have tried this problem over and over but I cant seem to picture it. Therefore I'm having problems solving it. Please help! Thank You. Click here to see answer by venugopalramana(3286)

 Question 31477: RSTW is a rhombus. GIve the coordinates of S and T. In part (c) give the coordinates in a terms of a and c, without introducing any new variables. d. Use your figure in part (c) for a coordinate proof that the diagonals of a rhombus are perpendicular. Click here to see answer by venugopalramana(3286)

 Question 31474: the midpoint of the hypotnuse of a right triangle is equidistant from the vertices. given: angle MON is a right angle, P is the midpoint of MN Prove: MP= PN =OP Click here to see answer by venugopalramana(3286)

 Question 31469: use coordinate geometry to prove that the midpoints of the sides of a kite determine a rectangle. given: kite DEFG, DE=EF, DG=GF, K, L,M and N are midpoints of the indicated sides Prove: KLMN is rectangle Click here to see answer by ikdeep(226)

 Question 31470: use coordinate geometry to prove that the midpoints of the sides of a kite determine a rectangle. given: kite DEFG, DE=EF, DG=GF, K, L,M and N are midpoints of the indicated sides Prove: KLMN is rectangle Click here to see answer by ikdeep(226)
 Question 31470: use coordinate geometry to prove that the midpoints of the sides of a kite determine a rectangle. given: kite DEFG, DE=EF, DG=GF, K, L,M and N are midpoints of the indicated sides Prove: KLMN is rectangle Click here to see answer by venugopalramana(3286)

 Question 32977: Given: :Line segment AB is congruent to line segment AE. Given: Angle C is congruent to angle F Given: Line segment BD is congruent to line segment ED Prove: Line segment AC is congruent to line segment AF Click here to see answer by venugopalramana(3286)

 Question 33432: I am stuck on this proof. It is: Prove: If an Isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle. Given: Triangle ABC is isosceles; Segment CD is teh altitude to base Segment AB. To prove:Segment CD bisects Angle ACB This is a problem our teacher gave us to do and i don't understand how to write proofs and i was wondering if you could help me. Thank you Click here to see answer by stanbon(57246)

 Question 33738: Use an indirect proof to show that John exceeded the 55 mph speed limit if he left his house at 8:15 a.m. and arrived at his office 60 miles away at 9:00 a.m. Write the proof using the paragraph method. Click here to see answer by Paul(988)

 Question 33739: Given: In triangle ABC, angle B=120 degrees Prove: angle A is not equal to 60 degrees Plan: use and indirect proof. use the paragraph method to write it. Click here to see answer by venugopalramana(3286)

 Question 35101: using deductive methods prove that if n is an interger, n is greater than or equal to 2 , then f(n)= n cubed - n is always divisible by at least 6 Click here to see answer by venugopalramana(3286)

 Question 33947: Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle. Given: Triangle ABC is isoceles; Segment CD is the altitude to base Segment AB To Prove: Segment CD bisects angle C Plan: ?? Proof:?? I need to know what the plan would be and the proof, the statements and reasons. Click here to see answer by venugopalramana(3286)

 Question 37352: If M and N are the midpoints of sides AB and BC of Triangle ABC right angled at B, then prove that 4(AN^2+CM^2)=5AC^2 Click here to see answer by venugopalramana(3286)

 Question 37916: Hi, I am having trouble trying to figure out how to do this problem. I am in 9th grade geometry but we are do a review of Algebra/Coordinate Proof. The question is: Position and label a right isosceles triangle on the coordinate plane. Then prove that the segment joining the midpoint of the two legs of the right triangle is parallel to the hypotenuse. Thanks so much for your help- Will Click here to see answer by Earlsdon(6287)

 Question 38152: Question: Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. (State your plan and give a proof. Given: ABCD is a parallelogram with <1~= <2 To Prove: ABCD is a rhombus So I can see that angles 1 and 2 are equal. In theorm 5-13 says the diagonals are pependicular but there is only one and then therom 5-14 says that each diagnoal... bisects two angles of the rhombus. Am I making this too difficult or do I just need to state 5-14 Thanks Click here to see answer by venugopalramana(3286)

 Question 37585: PQRS in a parallelogram,Q and S are joined to any point M on the diagonal PR of the parallelogram.Prove that area of the triangle PQM=area of triangle PSM Click here to see answer by venugopalramana(3286)

 Question 41417: I have been given the following problem and can't seem to figure out the answer: You are given triangle abc, and and abc in that triangle is a right angle. You are also given pqrs is a rectangle inside the triangle, so that ps is parallel to ab. This problem is trying to prove that (PQ) squared is equal to AQ x BR Click here to see answer by venugopalramana(3286)

 Question 41826: hi can u hgelp me with this problem: suppose four people sit down at a table and each place is set with 3 pieces of cutlery. in total there are 4 knives 4 forks and 4 spoons on the table, but a mischievous butler has allocated hese 12 utensils at random. determine the probability that each person gets one of each utensil. Click here to see answer by Nate(3500)

 Question 41825: hi this is a problem i have been trying for a couple days now and cant seem to get the right answer. Cionsider 5 caards with both sides blank. on the 10 sides are written 5 english letters (A, B, C, D and E) and five numbers (1,2,3,4 and 5), one symbol per side. if the symbols weere assigned to a side randomly what is the proabilit that each card has an english letter on one side and a number on the other? Click here to see answer by AnlytcPhil(1276)

 Question 41874: I can't figure out the correct reason in this proof for #4. Can you help me? Here it is: 1. line segment GF is perpendicular to AC given 2. angles AGF and CGF are congruent given 3. line segments GF and GF are congruent reflexive property 4. triangles GFA and GFC are congruent (? HELP) 5. line segments AG and CG CPCTC 6. triangle AGC is isosceles a triangle is an isosceles triangle if 1 of its vertices is contained by a perpendicular bisector Click here to see answer by PaulAllen65270(19)

 Question 42324: I'm trying to give the coordinatates of the points of ths graph for B Click here to see answer by Nate(3500)

 Question 43533: HI,I'm trying to prove two angles are congruent without using equal measurement. One triangle AGC is split into a smaller triangle using a mid line to form the base of another triangle. This triangle is split to form two other triangles GBE and GDE. The only given I have is line segement GB is congruent to line segment GD. I'm to prove Click here to see answer by venugopalramana(3286)

 Question 43688: 3 vertices of a parallelogram are given, find the fourth Click here to see answer by Nate(3500)

 Question 46622: Given: Line Segment ON bisects angle JOH, Angle J is congruent to angle H Prove: Line segement JN is congruent to line segement HN 0 . . . . . . . . . . .).......(. J N H Hope this helpes (I tried to give an image :) ) Click here to see answer by gsmani_iyer(180)

 Question 48715: Prove that, if the rays that bisect a pair of alternate interior angles are parallel, then the lines are parallel. Click here to see answer by stanbon(57246)

 Question 49204: B is between A and C. AB = 2x - 3, BC = 3x + 1, AC = 7x - 8, find BC. I received a worksheet on the 2nd day of school. Please help I dont know where to begin with this one. Thanks Click here to see answer by Osran_Shri(18)

 Question 49791: Question:How can I write a formal proof of the theorem. "If the base angles of a triangle are congruent, then the triangle is isosceles" This was my proof that was incorrect. Given: angle DAB=DAC (told not base angles) STATEMENTS REASONS 1. angleDAB=angleDAC 1. Given 2. DA-DA 2. Reflexive Property 3. Triangle BAD=Triangle CAB 3. SSS 4. BD=ED 4. CPCTC 5. angleBAD=angle CAD 5. Converse Base Angle Theorem 6. AD bisect BC 6. Def. of an Isosceles Triangle 7. triangle ABD=Triangle ACD 7. Isosceles Triangle Could you please show me the correct way to prove this theorem? Click here to see answer by venugopalramana(3286)
 Question 49791: Question:How can I write a formal proof of the theorem. "If the base angles of a triangle are congruent, then the triangle is isosceles" This was my proof that was incorrect. Given: angle DAB=DAC (told not base angles) STATEMENTS REASONS 1. angleDAB=angleDAC 1. Given 2. DA-DA 2. Reflexive Property 3. Triangle BAD=Triangle CAB 3. SSS 4. BD=ED 4. CPCTC 5. angleBAD=angle CAD 5. Converse Base Angle Theorem 6. AD bisect BC 6. Def. of an Isosceles Triangle 7. triangle ABD=Triangle ACD 7. Isosceles Triangle Could you please show me the correct way to prove this theorem? Click here to see answer by AnlytcPhil(1276)

 Question 49793: My son is going to grade 8 his math homework is to "explain the midpoint of a line segment" and give examples of items in everyday use. Its a project type question which has to be done on a poster. Thanks for your help Regards Sultana Mir Click here to see answer by rapaljer(4667)

 Question 50429: My daughter has math homework i cannot help with. Geometry- Straight segments She needs to find out what "z" is... Y is the midpoint. y= -1,5 X= -4,3 What is z? Formula= x-x/2 y-y/2 Click here to see answer by venugopalramana(3286)