Chapter 4.2, Problem 43E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# Prove that the segment that joins the midpoints of two sides of a triangle has a length equal to one-half the length of the third side.(HINT: In the drawing, M N ¯ is extended to D , a point on C D ¯ . Also, C D ¯ is a parallel to A B ¯ .)

To determine

To prove:

The segment that joins the midpoints of two sides of a triangle has a length equal to one-half the length of the third side.

Explanation

Formal proof:

Statement:

The segment that joins the midpoints of two sides of a triangle has a length equal to one-half the length of the third side.

Drawing:

Given:

ABC is a triangle with M and N as the midpoint of the sides AB and AC respectively.

ANâ‰…CN

AMâ‰…BM

Prove:

MN=12BC

 PROOF Statement Reasons 1. AMÂ¯â‰…BMÂ¯ANÂ¯â‰…CNÂ¯ 1. Given 2. Produce MN to D to meet CD which is parallel to AB. 2. Construct a parallelogram BCDM 3

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