In the adjoining figure, $A B C D$ is a square. if $∠ P Q R = 90^{o}$ and $P B = Q C = D R$ . Prove that
$P Q = Q R$

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Solution

Consider $△ P B Q$ and $△ Q C R$

It is given that $P B = Q C$

Since $A B C D$ is a square we get

$∠ P B Q = ∠ Q C R = 90^{o}$

By SAS congruence criterion

$△ P B Q ≅ Q C R$

$P Q = Q R$ (c.p.c.t)

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Similar questions

In the given figure, ABCD is a square and $∠ P Q R = 90^{\circ}$ . If PB = QC = DR, prove that (i) QB = RC, (ii) PQ = QR, (iii) $∠ Q P R = 45^{\circ}$

Q. In Fig. 6, ABCD is a square. If ∠PQR = 90° and PB = QC = DR, prove that ∠QPR = 45°.

Q. In the given figure,

P Q R S

is a square and

∠ B A C = 90^{o}

. Prove that

: R S^{2} = B R x S C

Q. In the adjoining figure,

A B C D

is a square and

△ E D C

is an equilateral triangle. Prove that

∠ D A E = 15^{o}

Q. Calculate the area of the quadrilateral

P Q R S

shown in the adjoining figure, given that

P Q = 8 c m, R Q = 17 c m, ∠ R P Q = 90^{o}, R S = 6 c m

and

∠ P R S = 90^{o}

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In the adjoining figure, ABCD is a square. if ∠PQR=90o and PB=QC=DR. Prove thatPQ=QR

Consider △PBQ and △QCRIt is given that PB=QCSince ABCD is a square we get ∠PBQ=∠QCR=90oBy SAS congruence criterion△PBQ≅QCRPQ=QR (c.p.c.t)

In the adjoining figure, $A B C D$ is a square. if $∠ P Q R = 90^{o}$ and $P B = Q C = D R$ . Prove that
$P Q = Q R$

Consider $△ P B Q$ and $△ Q C R$

It is given that $P B = Q C$

Since $A B C D$ is a square we get

$∠ P B Q = ∠ Q C R = 90^{o}$

By SAS congruence criterion

$△ P B Q ≅ Q C R$

$P Q = Q R$ (c.p.c.t)