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Which of the following pairs of triangles are congruent?

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ΔABC and ΔDEF in which AB = PQ, BC = QR and ∠C=∠R

ΔABC and ΔLMN in which ∠A = ∠L =

90^{0}

, AB = LM, ∠C =

40^{0}

and ∠M =

50^{0}

ΔABC and ΔDEF in which ∠B = ∠E =

50^{0}

, AC = DF

None

answer is B.

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Detailed Solution

Here, we need to find congruence between the given triangles.
Now in option (1),
ΔABC and ΔDEF in which AB = PQ, BC = QR and ∠C = ∠R.
So, the figure for these triangles is
4457(1.jfif

From the figure we can see that the given triangles are not congruent.
Also, in option (2)
ΔABC and ΔLMN are given in which ∠A = ∠L =

90^{0}

, AB = LM , ∠C=

40^{0}

and ∠M =

50^{0}

.
In ΔABC , ∠A =

90^{0}

and ∠C =

40^{0}

and the sum of all angles of a triangle is

180^{0}

.
∴ ∠A + ∠B + ∠C =

180^{0}

∴

80^{0}

+ ∠B +

40^{0}

180^{0}

∴ ∠B =

180^{0}

−

80^{0}

−

40^{0}

∴ ∠B =

60^{0}

s
And in ΔLMN, ∠L =

90^{0}

and ∠M =

50^{0}

and the sum of all angles of a triangle is

180^{0}

.
∴ ∠L + ∠N + ∠M =

180^{0}

∴

90^{0}

+ ∠N +

50^{0}

180^{0}

∴ ∠N =

180^{0}

−

90^{0}

−

50^{0}

∴ ∠N =

40^{0}

So, the figure for these triangles is
seo

Thus, from the figure we can say that the triangles ΔABC and ΔDEF are congruent to each other by AAA postulate.
So, ΔABC ≅ ΔLMN.
In option (3) two triangles ΔABC and ΔDEF are given in which ∠B = ∠E =