Question

pqrs is a rectangle.A and B on side PQ and SR respectively such that BQ=AR .Show that AQ=AR and angle BOR=ARQ

Answer 1

Hope this helps.....

Answer 2

Given : pqrs is a rectangle.

A and B on side PQ and SR respectively such that BQ=AR .

To Find : Show that AQ=BR and angle BOR=ARQ

Solution:

pqrs is a rectangle.

=> ∠Q = ∠R = 90°

A and B on side PQ and SR

=> ∠AQR  = ∠BRQ = 90°

in ΔAQR  and ΔBRQ

QR = RQ  ( common)

∠AQR  = ∠BRQ = 90°

AR = BQ   given

=> ΔAQR  ≅  ΔBRQ      (  RHS )

AQ = BR       CPCT

∠ARQ = ∠BQR

QED

Hence proved

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