Question

$\overline{WX}$and $\overline{YZ}$are perpendicular bisectors of each other.

Name four isosceles triangles.

Short answer

There arefour Isosceles Triangles namely $\Delta WXY,\Delta WXZ,\Delta YXZ,\Delta YWZ$.

Step-by-step solution

Step 1.  Define Perpendicular Bisector

A perpendicular bisector of a segment is a line or a ray or a segment that is perpendicular to the segment and passes through its midpoint.

Step 2.  Define an Isosceles Triangle

An isosceles triangle has two equal sides and two equal angles.

Step 3.  Write the pairs of congruent triangles 

Since, it is given that $\overline{WX}$and $\overline{YZ}$ are perpendicular bisectors of each other, so,

Wis equidistance from Yand Z. $\Rightarrow WY=WZ$

Zis equidistance from Wand X. $\Rightarrow WZ=XZ$

Yis equidistance from Wand X. $\Rightarrow YW=YX$

Xis equidistance from Zand Y. $\Rightarrow XY=XZ$

Thus,$\Delta WXY,\Delta WXZ,\Delta YXZ,\Delta YWZ$ are isosceles triangles.

Therefore, there are four Isosceles Triangles.