Question

Are the triangles below congruent? Give the reason.

Answer 1

In ΔABC, ∠A = 70°, ∠B = 60° and AB = 3.5 cm

By angle sum property, we have:

∠A + ∠B + ∠C = 180°

⇒ 70° + 60° + ∠C = 180°

⇒ 130° + ∠C = 180°

⇒ ∠C = 180° − 130° = 50°

In ΔPQR, ∠P = 70°, ∠R = 50° and PQ = 3.5 cm

Using angle sum property, we have:

∠P + ∠Q + ∠R = 180°

⇒ 70° + ∠Q + 50° = 180°

⇒ 120° + ∠Q = 180°

⇒ ∠Q = 180° − 120° = 60°

⇒ ∠C = ∠Q …(1)

Now, in ΔABC and ΔPQR:

∠A = ∠P (Given)

AB = PQ (Given)

∠C = ∠Q (From equation (1))

As the two angles and the included side are equal to the two angles and the included side of the other triangle, ΔABC ≅ ΔPQR.