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Question

Quadrilateral ABCD is a square. P, Q and R are the points on AB, BC and CD respectively, such that AP=BQ=CR. Hence,.If PQR is a right angle, find PRQ(in degrees)

Solution
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Given: ABCD is a square.
thus, AB=BC
AP=BQ (Given)
ABAP=BCBQ
PB=CQ (I)
Now, In PBQ and CQR,
PBQ=QCR (Each 90)
PB=CQ (From I)
BP=CR (Given)
thus, PBQCQR (SAS rule)
or, PQ=QR (By cpct)
Now, In PQR
PQ=QR
thus, PRQ=QPR=x (Isosceles triangle property)
PQR=90 (Given)
Sum of angles = 180
PQR+QPR+QRP=180
90+x+x=180
2x=90
x=45
Thus, PRQ=45

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