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Zigmanuir [339]
2 years ago
9

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

Mathematics
1 answer:
andrey2020 [161]2 years ago
7 0

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}]

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