Question

determine if triangle ( pqr ) and triangle ( stu ) are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles similar.

Explanation:

Step1: Calculate the third angle of triangle \(PQR\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle PQR\), let the third angle be \(x\). Then \(x + 71^{\circ}+47^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(71^{\circ}+47^{\circ})=62^{\circ}\).

Step2: Check for angle - angle similarity

In \(\triangle PQR\), the angles are \(47^{\circ},62^{\circ},71^{\circ}\). In \(\triangle STU\), the angles are \(47^{\circ},62^{\circ}\). Since two angles of \(\triangle PQR\) (\(47^{\circ}\) and \(62^{\circ}\)) are equal to two angles of \(\triangle STU\) (\(47^{\circ}\) and \(62^{\circ}\)), by the AA (angle - angle) similarity criterion.

Answer:

The triangles are similar (by AA similarity criterion).