   Chapter 4.4, Problem 35E 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

In exercises 29 to 35, complete a formal proof.Given: E F ¯ is the median of trapezoid ABCD.Prove: E F = 1 2 ( A B + D C ) .(HINT: Using theorem 4.4.7, show that M is the midpoint of A C ¯ . For Δ A D C         a n d           Δ C B A apply theorem 4.2.5) Exercises 35-37

To determine

To Prove:

EF=12(AB+DC)

Explanation

Consider the following diagram.

Given: EF¯ is the median of the trapezoid ABCD.

Prove: EF=12(AB+DC).

Plan: Draw a transversal AC¯ through M.

Here, AB||EF||DC.

We know that, three parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any transversal.

It means AMMC.

Therefore, M is the midpoint of AC¯

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