Question

are these triangles similar? yes no

Explanation:

Step1: Recall similarity - angle criterion

Two triangles are similar if two pairs of corresponding angles are equal.

Step2: Find the third - angle of $\triangle PQR$

The sum of angles in a triangle is $180^{\circ}$. In $\triangle PQR$, let the third - angle be $\angle P$. Then $\angle P=180^{\circ}-(52^{\circ} + 96^{\circ})=180^{\circ}-148^{\circ}=32^{\circ}$.

Step3: Find the third - angle of $\triangle TUV$

In $\triangle TUV$, let the third - angle be $\angle V$. Then $\angle V=180^{\circ}-(52^{\circ}+85^{\circ})=180^{\circ}-137^{\circ}=43^{\circ}$.

Step4: Compare the angles

The angles of $\triangle PQR$ are $32^{\circ},52^{\circ},96^{\circ}$ and the angles of $\triangle TUV$ are $43^{\circ},52^{\circ},85^{\circ}$. Since the corresponding angles are not equal, the triangles are not similar.

Answer:

no