Chapter 8, Problem 5MCQ

To determine

The similarity statement of the three similar triangles.

Answer to Problem 5MCQ

  $\Delta PQR\cong \Delta QSR\cong \Delta PSQ$

Explanation of Solution

Given:

The given figure is:

Calculation:

Angles:

  $\begin{array}{l}\angle QSP=\angle QSR=\angle PQR\\ \angle QPR=\angle QPS=\angle SQR\\ \angle PRQ=\angle QRS=\angle PQAS\end{array}$

Sides:

  $\begin{array}{l}\overline{QR}\cong \overline{PR}\cong \overline{PQ}\\ \overline{QR}\cong \overline{SR}\cong \overline{SQ}\\ \overline{QS}\cong \overline{PQ}\cong \overline{PS}\end{array}$

Therefore,

  $\Delta PQR\cong \Delta QSR\cong \Delta PSQ$