Question

determine whether the triangles are similar. if so, write a similarity statement and name the postulate or theorem you used. if not, explain. choose the correct answer below. a. yes, △sor ~ △wok because ∠s ≅ ∠w and ∠sor ≅ ∠wok. thus, the triangles are similar by the aa - postulate. b. yes, △sor ~ △wok because ∠s ≅ ∠w and \\(\frac{ro}{ko}=\frac{so}{wo}\\). thus, the triangles are similar by the sas - theorem. c. yes, △sor ~ △wok because \\(\frac{ro}{ko}=\frac{so}{wo}=\frac{rs}{wk}\\). thus, the triangles are similar by the sss - theorem. d. no, the triangles are not similar because no theorem or postulate can be satisfied.

Explanation:

Step1: Identify angle - angle similarity

We know that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar by the AA - postulate. In the given triangles, we can see that $\angle S\cong\angle W$ (marked with the same angle - marking) and $\angle SOR\cong\angle WOK$ (vertically - opposite angles are congruent).

Step2: Check similarity statements

The similarity statement for similar triangles $\triangle SOR$ and $\triangle WOK$ based on the AA - postulate is $\triangle SOR\sim\triangle WOK$.

Answer:

A. Yes, $\triangle SOR\sim\triangle WOK$ because $\angle S\cong\angle W$ and $\angle SOR\cong\angle WOK$. Thus, the triangles are similar by the AA - postulate.