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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

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.

ANCN

AMBM

Prove:

MN=12BC

PROOF
Statement Reasons
1. AM¯BM¯
AN¯CN¯
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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