Question

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

Explanation:

Step1: Calculate the ratio of corresponding sides

For triangle \(MNO\) and \(PQR\), \(\frac{30}{15}=\frac{42}{21} = 2\).

Step2: Check the included angle

The included angle of the sides in \(\triangle MNO\) and \(\triangle PQR\) is \(53^{\circ}\) (given).

Answer:

The triangles are similar because the ratios of two pairs of corresponding sides are equal (\(\frac{30}{15}=\frac{42}{21} = 2\)) and the included angles are equal (\(53^{\circ}\)), so by the Side - Angle - Side (SAS) similarity criterion, \(\triangle MNO\sim\triangle PQR\).