Question

△pqt and △rst are shown below. which statement is true? △pqt is similar to △rst. △pqt is not similar to △rst. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find the third angle of \(\triangle PQT\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle PQT\), let the third angle be \(x\). Then \(x + 52^{\circ}+91^{\circ}=180^{\circ}\). So \(x=180^{\circ}-(52^{\circ} + 91^{\circ})=37^{\circ}\).

Step2: Find the third angle of \(\triangle RST\)

For \(\triangle RST\), let the third angle be \(y\). Then \(y+52^{\circ}+36^{\circ}=180^{\circ}\). So \(y = 180^{\circ}-(52^{\circ}+36^{\circ}) = 92^{\circ}\).

Step3: Check similarity

Since the angles of \(\triangle PQT(52^{\circ},91^{\circ},37^{\circ})\) and \(\triangle RST(52^{\circ},36^{\circ},92^{\circ})\) are not equal, the triangles are not similar.

Answer:

\(\triangle PQT\) is not similar to \(\triangle RST\).