Question

For the following figure, X, Y, Z are the midpoints of the sides of isosceles $\Delta ABC$. Explain why XZBA is a trapezoid.

Short answer

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

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

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

Consider the triangle $\Delta ABC$.

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

Step 3. Step description.

Now, the side $\overline{XZ}$is parallel to the third side $\overline{AB}$such that $\overline{XZ}\parallel \overline{AB}$.

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

Thus, $XZBA$is a trapezoid.