Chapter 3.7, Problem 24PSC

To determine

To prove : $\Delta YTO$ is isosceles.

Explanation of Solution

Given information : The following information has been given

XSTOW is equilateral and equiangular

Formula used : For regular polygons, all the sides and angles are congruent

Proof : We know that if XSTOW is equilateral and equiangular, then it is a regular pentagon. Thus, now we can say that in triangles STO and WTO,

  $\overrightarrow{ST}\cong \overrightarrow{WO}$

  $\overrightarrow{TO}\cong \overrightarrow{OT}$

  $\angle STO\cong \angle WOT$

So, we can say that $\Delta STO\cong \Delta WOT$ . Thus, now we can say that

  $\angle SOT\cong \angle WTO$

Hence, in $\Delta YTO$ we can say that

  $\angle YOT\cong \angle YTO$

Thus, we can say that $\Delta YTO$ is isosceles