CONGRUENCE OF SIMPLE POLYGONS B11

 If PQ = RS and PQRS is a straight line, Prove that <UPQ = <RST

Solution

Given: figure PQTSRU.

Required to prove: <UPQ and <RST are equal.

Proof: PQ= RS    (given)

TQ= RU (equal sides)  

PU = TS (equal sides)

PQ + QR = QR + RS  (equal sides)

Hence ∆PRU and ∆TQS are congruent by SSS rule.

Therefore <UPQ = <RST Proved!