Question

here are triangles lmn and pqr. are the triangles similar? choose your answer from the drop - down menu. if so, write a similarity statement. if not, ignore this box.

Explanation:

Step1: Calculate the third angle of triangle LMN

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle LMN\), if \(\angle L = 60^{\circ}\) and \(\angle M=70^{\circ}\), then \(\angle N=180^{\circ}-(60^{\circ} + 70^{\circ})=50^{\circ}\)

Step2: Compare angles of the two triangles

In \(\triangle LMN\), angles are \(60^{\circ},70^{\circ},50^{\circ}\). In \(\triangle PQR\), angles are \(60^{\circ},50^{\circ}\) (given \(\angle Q = 60^{\circ},\angle R=50^{\circ}\)), and \(\angle P=180^{\circ}-(60^{\circ}+50^{\circ}) = 70^{\circ}\)
Since all three pairs of corresponding angles are equal (\(\angle L=\angle Q = 60^{\circ}\), \(\angle M=\angle P=70^{\circ}\), \(\angle N=\angle R = 50^{\circ}\)), by the AA (Angle - Angle) similarity criterion, the triangles are similar.

Answer:

\(\triangle LMN\sim\triangle QPR\)