   Chapter 4.CR, Problem 25CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

Review Exercises Given: A B C D is a ▱ A F - ≅ C E - Prove: D F - ∥ E B - To determine

To Prove:

In the provided parallelogram ABCD, DF-EB- based on the information given.

Explanation

Theorem on parallel lines:

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

Calculation:

It is given that ABCD is a parallelogram with AF-CE-.

By the theorem on parallel line, two parallel lines DC and AB are cut by a transversal line AC (diagonal), alternate interior angles mCAD=mACB.

Since ABCD is a parallelogram, AD=BC. Also given that AF=CE.

For BAF and BCE, the sides AD and BC and angles mCAD and mACB are congruent.

Here two sides and one angle are common to both the triangles.

Therefore, both are congruent triangles

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