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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Review Exercises

Given: A B E F is a rectangle
B C D E is a rectangle
F E - = E D -
Prove: A E - B D -   and   A E - B D -

To determine

To Prove:

For the provided rectangles ABEF and BCDE, AE-BD- and AE-BD- with the help of the given information

Explanation

Proof:

Theorem on parallel lines:

If two lines are cut by a transversal line and the alternate exterior angles are congruent, the lines are parallel.

Description:

It is given that ABEF and BCDE are rectangle attached to each other as shown in the picture with FE-=ED-.

Since FE-=ED-, rectangles ABEF and BCDE have common base and height.

Hence the rectangle ABEF and the rectangle BCDE are congruent.

Since the rectangles are congruent, their diagonals must be same.

This implies AE-BD-.

Considering the line BE as a transversal line for the lines AE and BD with its same alternate interior angles (mDBE=mBEA), it can conclude from the theorem that these lines are parallel to each other

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