(a) In the given figure, prove that:

(i) PQ = RS

(ii) PS = QR

(b) Which congruence criterion will you use in the following?

(i) Given: ∠ MLN = ∠ FGH
∠ NML = ∠ GFH

ML = FG

So, ΔLMN ≅ ΔGFH

(ii) Given: EB = DB

AE = BC

∠ A = ∠ C = 90°

So, ΔABE ≅ ΔCDB
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[4 MARKS]

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Solution

Each part: 2 Marks

(a) In $Δ P S R$ and $Δ R Q P$

$∠ P S R = ∠ R Q P$ [Given]

$∠ S P R = ∠ Q R P$ [Given]

$P R = P R$ [Common]

$\Rightarrow Δ P S R ≅ Δ R Q P$ [AAS congruency criteria]

(i) $∴ P Q = R S$ [Corresponding parts of congruent triangles]

(ii) Also, $P S = Q R$ [Corresponding parts of congruent triangles]

(b) (i) ASA, as two angles and the side included between these angles of ΔLMN, are equal to two angles and the side included between these angles of ΔGFH.

(ii) RHS, as in the given two right-angled triangles, one side and the hypotenuse are respectively equal.

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Similar questions

Which congruence criterion do you use in the following?

(a) Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

(b) Given: ZX = RP

RQ = ZY

∠PRQ = ∠XZY

So, ΔPQR ≅ ΔXYZ

∠NML = ∠GFH

ML = FG

So, ΔLMN ≅ ΔGFH

(d) Given: EB = DB

AE = BC

∠A = ∠C = 90°

So, ΔABE ≅ ΔCDB

∠ A = ∠ C = 90^{\circ}

∠ M L N = ∠ F G H, ∠ N M L = ∠ H F G, M L = F G

Δ L M N ≅ Δ G F H

∠ M L N = ∠ F G H, ∠ N M L = ∠ H F G, M L = F G

Δ L M N ≅ Δ G F H

Which congruence criterion is used in the following?

Given: $∠ M L N = ∠ F G H, ∠ N M L = ∠ H F G, M L = F G$
So, $Δ L M N ≅ Δ G F H$

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