Chapter 10.4, Problem 13E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

*In Exercises 1 to 17, complete an analytic proof for each theorem.*

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

To determine

**To answer:**

The analytic proof for the given theorem “The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side”.

Explanation

Given theorem is,

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

The above figure shows the triangle ABC.

The vertices of the triangle ABC is A

D and E are the midpoints of the sides AC and BC.

Now, joining the points D and E as shown in the figure.

Hence, the line DE is parallel to the third side of the triangle AB.

Based on the midpoint formula,

The midpoint of AC

The midpoint of AC

Similarly, midpoint of BC

The midpoint of BC

Based on the distance formula, the length of DE which has the coordinates of D

DE

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