PQRS is a square and ABC=90 degrees shown in the figure If AP=BQ=CR , then prove that - Maths - Quadrilaterals

Question

PQRS is a square and <ABC=90 degrees shown in the figure If
AP=BQ=CR , then prove that <BAC=45 degrees

Anuradha Sharma · Accepted Answer

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Here AP=BQ=RC
1Also PQ=QRSo PB+BQ=QC+CRPB=QC using equation 1Now in triangle APB and BQC, AP = BQ PB=QC ∠APB=∠BQC=90 degreeSo ∆APB ≅∆ BQC SAS congruencySO AB = BC∠BAC=∠BCASo in triangle ABC, 90+∠BAC+∠BCA=180∠BAC=∠BCA=45 degree

PQRS is a square and <ABC=90 degrees shown in the figure. If AP=BQ=CR , then prove that <BAC=45 degrees