Question

R is the midpoint of PQ.Angle PRS = angle QRT and angle RPT=angle RQS.prove that triangle RPT= triangle RQS and PT=QS

Answer 1

Step-by-step explanation:

in triangle PQR, PQ=PR ( given)

angle PRQ = angle PQR ( angle opposite to the equal sides are equal ) .....( 1 )

since, ST ll QR and PQ is a transversal than angle PQR = PST ( corresponding angles ) .....( 2 )

since, PQ ll QR and PR is a transversal , then angle PRQ = angle PST ( corresponding angles ) .....( 3 )

but angle PQR = angle PRQ , then from ( 2 ) and ( 3 ) we get

angle PST = angle PTS

in triangle PST

angle PST = angle PTS ( proved )

therefore , PT = PS ( sides opposite to equal sides are equal )

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