Chapter 5.5, Problem 2CE

To determine

To identify: two trapezoids other than $XZBA$ .

Answer to Problem 2CE

$ACZY$ And $BCXY$

Explanation of Solution

Given:

The diagram:

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

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

Consider the figure shown below:

Consider the triangle $△ABC$ .

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

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

  $\overline{YZ}\parallel \overline{AC}$

So, $ACZY$ is a quadrilateral with exactly one pair of sides $\overline{YZ}$ and $\overline{AC}$ parallel.

So, by definition $ACZY$ is a trapezium.

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

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

  $\overline{XY}\parallel \overline{BC}$

So, $BCXY$ is a quadrilateral with exactly one pair of sides $\overline{XY}$ and $\overline{BC}$ parallel.

So, by definition $BCXY$ is a trapezium.