   Chapter 4.CR, Problem 27CR ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# Review Exercises Given: D E is a median of ∆ A D C B E - ≅ F D - E F - ≅ F D - Prove: A B C D is a ▱ To determine

To Prove:

The provided quadrilateral ABCF is a parallelogram.

Explanation

Proof:

Definition:

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle’s centroid.

Theorem on parallelogram:

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Description:

It is given that DE is a median of ADC with BE-FD- and EF-FD-.

BE-FD-EF-. That is, BE-EF-

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