Chapter 4, Problem 17CT

To determine

To name: thefour isosceles triangles of the given figure.

Answer to Problem 17CT

  $\Delta WXY,\Delta WXZ,\Delta YXZ,\Delta YWZ$

Explanation of Solution

Given information:

The given figure is as follows:

  

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

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

The perpendicular bisector of line is a perpendicular line passing through midpoint of that

line.

So,

W is equidistance from Y and Z . $\Rightarrow WY=WZ$

Z is equidistance from Wand X . $\Rightarrow WZ=XZ$

Y is equidistance from Wand X . $\Rightarrow YW=YX$

X is equidistance from Z and Y . $XY=XZ$

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

Hence, the four isosceles triangles are $\Delta WXY,\Delta WXZ,\Delta YXZ,\Delta YWZ$.