Question

1. sas

a) ∠q≅∠b
b) rs≅rd or sq≅db
c) ∠qrs≅∠brd
d) rs≅rd

Explanation:

Step1: Recall SAS criterion

SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In the given figure, we already have one pair of sides ($QR = BR$ and $SR=DR$ as marked). For $\triangle QRS$ and $\triangle BRD$ to be congruent by SAS, we need the included angles between these pairs of sides to be congruent. The included angle for sides $QR$ and $SR$ in $\triangle QRS$ is $\angle QRS$, and for sides $BR$ and $DR$ in $\triangle BRD$ is $\angle BRD$. So we need $\angle QRS\cong\angle BRD$.

Answer:

C. $\angle QRS\cong\angle BRD$