Which of the following pairs of triangles are congruent ?

(a) △ABC and △DEF in which : BC = EF, AC = DF and ∠C = ∠F.

(b) △ABC and △PQR in which : AB = PQ, BC = QR and ∠C = ∠R.

(c) △ABC and △LMN in which : ∠A = ∠L = 90°, AB = LM, ∠C = 40° and ∠M = 50°

(d) △ABC and △DEF in which : ∠B = ∠E = 90°, AC = DF

(a) In △ABC and △DEF,

⇒ BC = EF [Given]

⇒ AC = DF [Given]

⇒ ∠C = ∠F [Given]

∴ △ABC ≅ △DEF (By S.A.S axiom)

Hence, △ABC and △DEF are congruent by S.A.S axiom.

(b) Given,

In △ABC and △PQR,

⇒ AB = PQ [Given]

⇒ BC = QR [Given]

⇒ ∠C = ∠R [Given]

Here the equal angles are not the included angles, thus the triangles are not necessarily congruent.

Hence, △ABC and △PQR are not necessarily congruent.

(c) Given,

In △ABC,

⇒ ∠A + ∠B + ∠C = 180°

⇒ 90° + ∠B + 40° = 180°

⇒ ∠B + 130° = 180°

⇒ ∠B = 180° - 130°

⇒ ∠B = 50°.

In △ABC and △LMN,

⇒ AB = LM [Given]

⇒ ∠B = ∠M [Both equal to 50°]

⇒ ∠A = ∠L [Both equal to 90°]

∴ △ABC ≅ △LMN (By A.S.A axiom)

Hence, △ABC and △LMN are congruent by A.S.A axiom.

(d) Given,

In △ABC and △DEF,

⇒ ∠B = ∠E = 90°

⇒ AC = DF

⇒ AB = DE

∴ △ABC ≅ △DEF (By R.H.S. axiom)

Hence, △ABC and △DEF are congruent by R.H.S. axiom.