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Elementary Geometry for College St...

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

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Prove that the line segment joining the midpoints of two sides of a triangle determines a triangle that is similar to the original triangle.

To determine

To prove:

The statement “The line segment joining the midpoints of two sides of a triangle determines a triangle that is similar to the original triangle.”

Explanation

Definition:

SSS:

If the three sides of one triangle are proportional (in length) to the three corresponding sides of a second triangle, then the triangle are similar.

Description:

Draw the line segment joining the midpoints of two sides as shown below.

Figure

From the given figure, it is observed that the line segment DE joining the two sides of AB and AC. In the triangle ABC, D is the midpoint of AB and E is the midpoint of AC.

By the definition of midpoint, AD=12AB and AE=12AC.

It is known that the line segment DE joins the midpoints of two sides a triangle, its length DE is half the length of BC. That is, DE=12BC

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