Question

given: $overline{pr}$ bisects $angle qps$, $pq = 12$ units, and $ps = 12$ units. prove: $overline{qr}congoverline{sr}$. how could you show $overline{qr}congoverline{sr}$? a. use sas to show triangle $prq$ is congruent to triangle $srp$. b. use aas to show triangle $prq$ is congruent to triangle $prs$. c. use asa to show triangle $prq$ is congruent to triangle $prs$. d. use sas to show triangle $prq$ is congruent to triangle $prs$.

Explanation:

Step1: Analyze given conditions

已知$\overline{PR}$平分$\angle QPS$，则$\angle QPR=\angle SPR$；又$PQ = 12$，$PS = 12$，即$PQ = PS$，且$PR$为公共边。

Step2: Determine congruence - criterion

两边及其夹角对应相等（$PQ = PS$，$\angle QPR=\angle SPR$，$PR = PR$），符合$SAS$（边角边）全等判定定理，可证$\triangle PRQ\cong\triangle PRS$。

Step3: Get the result

全等三角形对应边相等，所以$\overline{QR}\cong\overline{SR}$，应选D。

Answer:

D. Use SAS to show triangle PRQ is congruent to triangle PRS