Chapter 5, Problem 18CUR

To determine

To complete: the given statement about the diagram.

Answer to Problem 18CUR

  $\overline{BE}$ is a median of $\Delta ABC$ .

Explanation of Solution

Given information:

Given figure,

  

Given:

  $ABCD$ is a parallelogram;

  $\overline{AD}\cong \overline{AC}$ ; $\overline{AE}\cong \overline{EC}$

  $\angle ADF\cong \angle CDF$ ; $m\angle DAC=36$ .

Given statement,

  $\overline{AE}\cong \overline{EC}$ , So $\overline{BE}$ is a -------- of $\Delta ABC$ .

Calculation:

Observe the parallelogram $ABCD$ , see that $\overline{AD}\cong \overline{AC}\cong \overline{AE}\cong \overline{EC}$ .

Hence look at the triangle $\Delta ABC$ of this parallelogram point $E$ is midpoint of segment $\overline{AC}$ .

As median of a triangle is segment from a vertex to the midpoint of opposite side.

Thus, if $\overline{AE}\cong \overline{EC}$ ,

Hence, $\overline{BE}$ is a median of $\Delta ABC$ .