Chapter 4.3, Problem 3WE

To determine

Toprove: $\angle W\cong \angle Z$, if $\overline{WO}\cong \overline{ZO};\overline{XO}\cong \overline{YO}$

  

Explanation of Solution

Given information :

Given $\overline{WO}\cong \overline{ZO};\overline{XO}\cong \overline{YO}$.

  

Proof: Given $\overline{WO}\cong \overline{ZO};\overline{XO}\cong \overline{YO}$ and $\angle WOX=\angle ZOY$ as they are vertical angles By Side-Angle- Side (SAS) theorem, the given two triangles are congruent.

Thus, $\Delta OXW\cong \Delta OYZ$

  $\Rightarrow$ the two triangles will have exactly the same three sides and exactly the same three angles.

Hence, $\angle W\cong \angle Z$.