Question

are these triangles similar? yes no

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \).
For \( \triangle QRP \), let the third angle be \( \angle P \).
\( \angle P=180^{\circ}-(37^{\circ} + 88^{\circ})=180^{\circ}-125^{\circ} = 55^{\circ} \)

Step2: Calculate the third angle of triangle \( HIG \)

For \( \triangle HIG \), let the third angle be \( \angle I \).
\( \angle I=180^{\circ}-(31^{\circ}+88^{\circ})=180^{\circ}-119^{\circ}=61^{\circ} \)

Step3: Check for similarity

Two triangles are similar if their corresponding angles are equal.
Since \( 37^{\circ}
eq31^{\circ} \), \( 55^{\circ}
eq61^{\circ} \), the triangles are not similar.

Answer:

no