SOLUTION: I need to write an indirect proof for this problem: Given- AB is not equal to DE & AC is congruent to CD Prove measure of angle B is not equal to measure of angle e there is a

Algebra ->  Geometry-proofs -> SOLUTION: I need to write an indirect proof for this problem: Given- AB is not equal to DE & AC is congruent to CD Prove measure of angle B is not equal to measure of angle e there is a      Log On


   

Question 117985: I need to write an indirect proof for this problem:
Given- AB is not equal to DE & AC is congruent to CD
Prove measure of angle B is not equal to measure of angle e
there is a picture of two triangles facing each other and sharing one point- the tops of each triangle and the letters read from left to right- top left point A, middle point where both triangles meet point C, then next top point is point D, lower right point E, then C again, lower left point is point B.
Sorry if that isn't enought info. but thanks for your help.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
I need to write an indirect proof for this problem:
Given- AB is not equal to DE & AC is congruent to CD
Prove measure of angle B is not equal to measure of angle E
there is a picture of two triangles facing each other and sharing one point- the tops of each triangle and the letters read from left to right- top left point A, middle point where both triangles meet point C, then next top point is point D, lower right point E, then C again, lower left point is point B.
Sorry if that isn't enought info. but thanks for your help.



1. Assume for contradiction that mÐB = mÐE

2. AC @ CD    Given

3. mÐACB = mÐDCE  (opposite or vertical angles)      

4. DACB @ DDCE   (ASA, angle-side-angle by 1,2,and 3)

5. AB = DE      (corresponding sides of congruent triangles)

6. AB m DE      (given)

7.   5 and 6 contradict each other.

8. mÐB = mÐE (assumption in step 1 is false.)

Edwin