Question

determine whether the pair of triangles is similar. explain your reasoning. select choice select choice select choice yes no need help with this question? get a hint

Explanation:

Step1: Find angles in first triangle

In $\triangle SKM$, one angle is $60^{\circ}$ and one is $90^{\circ}$. Using the angle - sum property of a triangle ($180^{\circ}$ in a triangle), the third angle $\angle M=180^{\circ}-(90^{\circ} + 60^{\circ})=30^{\circ}$.

Step2: Compare angles with second triangle

In $\triangle QRT$, $\angle Q = 30^{\circ}$ and $\angle R=90^{\circ}$. The third angle $\angle T=180^{\circ}-(90^{\circ}+30^{\circ}) = 60^{\circ}$. The angles of $\triangle SKM$ are $30^{\circ},60^{\circ},90^{\circ}$ and the angles of $\triangle QRT$ are $30^{\circ},60^{\circ},90^{\circ}$. Since the corresponding angles of the two triangles are equal, by the AA (angle - angle) similarity criterion, the triangles are similar.

Answer:

Yes