Pick the option which matches the two columns.

(A) \to q; (B) \to s; (C) \to p; (D) \to r

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(A) \to q; (B) \to p; (C) \to r; (D) \to s

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(A) \to s; (B) \to p; (C) \to q; (D) \to r

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(A) \to s; (B) \to r; (C) \to p; (D) \to q

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Solution

The correct option is A $(A) \to q; (B) \to s; (C) \to p; (D) \to r$
$(A) \to q; (B) \to s; (C) \to p; (D) \to r$

(A) $In Δ P Q S and Δ P R S$
PQ = PR = 6 cm [Given]
PS = PS [Common]
$∠ P S Q = ∠ P S R = 90^{\circ}$
$\Rightarrow Δ P Q S ≅ Δ P R S$ (by R.H.S congruency)

(B) $In Δ P O Q and Δ R O S$ ,
$P Q = R S = 6 c m$
$∠ Q P O = ∠ S R O = 30^{\circ}$
$∠ P O Q = ∠ R O S$
(vertically opposite angles)
$\Rightarrow Δ P O Q ≅ Δ R O S$ (by AAS congruency)

(C) $In Δ P O R and Δ Q O S$ ,
$P O = Q O$ (Given)
$∠ P O R = ∠ Q O S$
(vertically opposite angles)
$R O = S O$ (Given)
$Δ P O R ≅ Δ Q O S$ (by SAS congruency)

(D) In $Δ P M Q a n d Δ P M R$ ,
$\begin{matrix} P Q = P R (g i v e n) Q M = R M (g i v e n) P M = P M (c o m m o n) \end{matrix}$
$\Rightarrow Δ P M Q ≅ Δ P M R$ (by SSS congruency)

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