Question

Q25. In the given figure, AB=PQ, BR=CQ, AB is perpendicular to BC, PQ is
perpendicular to RQ. Prove that AC=PR.
​

Answer 1

Step-by-step explanation:

Given:AB=PQ=BQ

In△ABC&△PQR

⟹AB=PQ

∠ABC=∠PQR=90

∘

BC=RQ

∴△ABC≅△PQR

⟹AC=PR(C.P.C.T)

In△ABR

AB

2

+BR

2

=AR

2

⟹AB

2

+(BC+CR)

2

=AR

2

−(1)

In△PCR:

⟹PQ

2

+QC

2

=PC

2

⟹PQ

2

+(QR+CR)

2

=PC

2

In(1)&(2),

∵AB=PQ(given)

andBC=QR(given)

⟹AR

2

=PC

2

(from(1)&(2))

AR=PC−(3)

In△ABR&△PQC

⟹AB=PQ

∠ABR=∠PQC=90

∘

AR=PC−(from(3))

∴△ABR≅△PQCbyR.H.S