Chapter 5, Problem 9CR

To determine

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

Answer to Problem 9CR

A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.

Explanation of Solution

Given information:

Given figure,

Given:

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

Calculation:

Also consider that $AE=EC=9$

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

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

Thus the principle theorem that justifies this given statement about the diagram is theorem 5-10 which is stated as “a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side”.