Chapter E, Problem 4.8EX

To determine

To Prove:

The two triangles are congruent.

Explanation of Solution

Given information:

$P\overline{O}\perp \text{ plane X}$ and $PT=PS$ in the given triangle.

The SAS rule states that, if two sides and included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

From the given figure,

The sides PT is parallel to the side PS and the side TO is parallel to the side SO .

If two corresponding sides are in the same ratio then their corresponding angles are equal.

$\angle POT$ and $\angle POS$ are ${90}^{\circ }$ .

Therefore, by SAS rule we can prove that the given two triangles are congruent.