Question

For the following figure, X, Y, Z are the midpoints of the sides of isosceles $\Delta ABC$. Name two trapezoids other than XZBA.

Short answer

The two trapezoids are $ACZY,BCXY$.

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

Step 3. Step description.

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

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

Therefore, $ACZY$is a trapezoid.

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

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

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

Therefore, $BCXY$is a trapezoid.

Thus, the two trapezoids are $ACZY$and $BCXY$.