Chapter 5, Problem 10CR

To determine

To state: the principal theorem that justifies the statement about the diagram.

Answer to Problem 10CR

The segment that joins the midpoint of two sides of a triangle is parallel to third side.

Explanation of Solution

Given information:

Given figure,

Given:

If $D$ is the midpoint of $\overline{AB}$ , then $\overline{DE}\parallel \overline{BC}$ .

Calculation:

Also consider that $D$ is the midpoint of $\overline{AB}$

Therefore, the point $E$ is the midpoint of $\overline{AC}$ .

Hence, the principal theorem that justifies the statement if $D$ is the midpoint of $\overline{AB}$ , then

  $\overline{DE}\parallel \overline{BC}$ about the diagram is “The segment that joins the midpoint of two sides of a triangle is parallel to third side”.