Question

in an isosceles trapezium mnop, mq and nr are perpendiculars to to po. show that triangle pqm= triangle orn and triangle pnr= triangle omq​

Answer 1

Answer:

Area of  Δ PQM = Area of Δ ORN , ∠PNR = ∠OMQ

Step-by-step explanation:

In an isosceles trapezium MNOP, MQ and NR are perpendiculars to PO.

MQ = NR  ( Perpendicular distance between parallel lines)

PM = ON  ( Isosceles trapezium)

∠PQM = ∠ORN = 90°

=> PQ = OR  

Area of  Δ PQM = (1/2) PQ * QM

Area of Δ ORN = (1/2) OR * RN

PQ = OR  *  QM = RN

=> Area of  Δ PQM = Area of Δ ORN

in Δ PNR  & ΔOMQ

RN = QM

PR = OQ   (PR = PQ + QR   = OR + QR = OQ)

∠PRN = ∠OQM = 90°

=> Δ PNR ≅ ΔOMQ

=> ∠PNR = ∠OMQ

QED

Proved

Step-by-step explanation:

Answer 2

Answer:

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