Question

are the two triangles similar? if yes, write a similarity statement and explain how you know they are similar.
choose the correct answer below.
a. yes, △rsb - △dse. the triangles are similar because ∠r≅∠d and (\frac{bs}{es}=\frac{rs}{ds}), which satisfies the sas - theorem.
b. yes, △rsb - △dse. the triangles are similar because ∠r≅∠d and ∠rsb≅∠esd, which satisfies the aa - postulate.
c. yes, △rsb - △dse. the triangles are similar because (\frac{bs}{es}=\frac{rs}{ds}=\frac{br}{ed}), which satisfies 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 see that $\angle R\cong\angle D$ and $\angle RSB\cong\angle ESD$ (vertical angles are congruent).

Step2: Recall AA - postulate

The AA (angle - angle) postulate states that if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.

Answer:

C. Yes, $\triangle RSB\sim\triangle DSE$. The triangles are similar because $\angle R\cong\angle D$ and $\angle RSB\cong\angle ESD$, which satisfies the AA - postulate.