Chapter 9, Problem 12CR

To determine

To prove:The congruency of $\angle R\&\angle S$

Explanation of Solution

Given information:The following information has been given

Circle with center Q lies in plane m

PQ is perpendicular to the plane m

Formula used:corresponding angles of congruent triangles are congruent

Proof:We know that in the right triangles PQR and PQS,

PQ is the common chord, hence congruent

QR and QS are the radii of the circle, hence congruent

  $\angle PQR\cong \angle PQS={90}^0$

Thus, by SAS rule, we can say that

  $\Delta PQR\cong \Delta PQS$

Now, we know that corresponding angles of congruent triangles are congruent. Thus, we can say that

  $\angle R\cong \angle S$