Question

determine whether the pair of triangles is similar. explain your reasoning. select choice skm is not congruent to ∠rqt △skm - △rtq by aa similarity △skm - △rqt by aa similarity

Explanation:

Step1: Find angles in $\triangle SKM$

In $\triangle SKM$, $\angle S = 90^{\circ}$, $\angle K=60^{\circ}$, so $\angle M=180^{\circ}-90^{\circ}-60^{\circ}=30^{\circ}$ by the angle - sum property of a triangle ($\sum_{i = 1}^{3}\angle_{i}=180^{\circ}$).

Step2: Compare angles with $\triangle RTQ$

In $\triangle RTQ$, $\angle R = 90^{\circ}$, $\angle Q = 30^{\circ}$, so $\angle T=180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ}$. We have $\angle M=\angle Q = 30^{\circ}$ and $\angle K=\angle T = 60^{\circ}$.

Step3: Apply AA similarity criterion

Since two pairs of corresponding angles are equal, by the AA (Angle - Angle) similarity criterion, $\triangle SKM\sim\triangle RTQ$.

Answer:

Yes, $\triangle SKM\sim\triangle RTQ$ by AA Similarity