Question

PQRS is an isosceles trapezium in which PQ RS and PS = RQ . if RT is drawn parallel to PS prove that​

Answer 1

Answer

Inequilateral△ERQ,∠REQ=∠EQR=∠QRE=60 °

GivenPQ∥SR,letRQbethetransversalthen∠SRQ+∠RQP=180°

{SumofInteriorcorrespondingangles=180 °}

Soweget∠SRQ=180−60=120 °

{∠RQP=∠EQR=60 °}

Weknowthatinaisoscelestrapeziumbaseanglesareequal.

So∠SPQ=∠RQP=60 °

GivenPQ∥SR,letSPbethetransversalthen∠RSP+∠SPQ=180°

{SumofInteriorcorrespondingangles=180 °}

Soweget∠RSP=180−60=120 °

∴Themeasuresofthetrapeziumare:∠RSP=120 °°

,∠SRQ=120 °

,∠RQP=60 °

,∠QPS=60 °

Thank you ☺️