Question

. In two triangles, ABC and PQR, ∠A = 30°, ∠B = 70°, ∠P = 70°, ∠Q = 80° and AB = RP, then
(a) ΔABC ≌ ΔPQR (b) ΔABC ≌ ΔQRP (c) ΔABC ≌ ΔRPQ (d) ΔABC ≌ ΔRQP

Answer 1

In two triangles, ABC and PQR,

∠A = 30°, ∠B = 70°,

∠P = 70°, ∠Q = 80° and AB = RP, then

• Draw 2 triangles ΔABC and ΔRPQ
• ∠A=30°, ∠B=70°, therefore, ∠C=80°
• ∠R=30°, because ∠P=70° and ∠Q=80°
• AB=RP as given
• Therefore, through ASA (Angle-Side-Angle) property, the triangles - ΔABC and ΔRPQ are congruent, since ∠A=∠R, AB=RP and ∠B=∠P

• Hence, (c) ΔABC ≌ ΔRPQ is the right answer.

Answer 2

Answer: ΔABC ≌ ΔRPQ

Step-by-step explanation:

Given: - ∠A = 30°, ∠B = 70°,

             ∠P = 70°, ∠Q = 80°

              AB = RP

Draw 2 triangles ΔABC and ΔRPQ

Angle: ∠A=30°, ∠B=70°, so, ∠C=80° due to Angle Sum Property

Side: AB=RP as given

Angle: ∠R=30°, ∠P=70° so, ∠Q=80° due to Angle Sum Property

ΔABC ≌ ΔRPQ [By ASA Congruence]