Question

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

In \(\triangle RSB\) and \(\triangle DSE\), we know that \(\angle RSB\) and \(\angle ESD\) are vertical angles, so \(\angle RSB\cong\angle ESD\). Also, given \(\angle R = 95^{\circ}\) and \(\angle D=95^{\circ}\), so \(\angle R\cong\angle D\).

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, then 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.