Chapter 5.5, Problem 1CE

To determine

To explain: why $XZBA$ is a trapezoid.

Answer to Problem 1CE

  $\overline{XZ}\parallel \overline{AB}$

Explanation of Solution

Given:

The diagram:

X, Z and Y are midpoints of the sides of isosceles $△ABC$ .

A trapezoid is a type of quadrilateral with one pair of parallel sides.

Consider the figure shown below:

Consider the triangle $△ABC$ .

Here, points X and Z are the mid points of $\overline{AC}$ and $\overline{BC}$ .

So, by theorem 5-11 part (1), the side $\overline{XZ}$ is parallel to the third side $\overline{AB}$ .

  $\overline{XZ}\parallel \overline{AB}$

So, $XZBA$ is a quadrilateral with exactly one pair of sides $\overline{XZ}$ and $\overline{AB}$ parallel.

So, by definition $XZBA$ is a trapezium.