Question

Given: <SPT = <RQT, ST = RT Prove: PR = QS​

Answer 1

Answer:

See explanation

Step-by-step explanation:

Consider triangles PTS and QTR. In these triangles,

• $ST=RT$ - given;
• $\angle SPT=\angle RQT$ - given;
• $\angle STP=\angle RTQ$ - as vertical angles when lines PR and SQ intersect.

Thus, $\triangle PTS\cong \triangle QTR$ by AAS postulate.

Congruent triangles have congruent corresponding sides, so

$PT=QT$

Consider segments PR and QS:

$PR=PT+TR\ [\text{Segment addition postulate}]\\ \\QS=QT+TS\ [\text{Segment addition postulate}]\\ \\PT=QT\ [\text{Proven}]\\ \\ST=RT\ [\text{Given}]$

So,

$PR=SQ\ [\text{Substitution property}]$