If ΔPQR ≅ ΔABC, AB = 6 cm, ∠B = 50° and ∠A = 70°, then which of the following is true?

Question

Accepted Answer

Given ΔPQR ≅ ΔABC, corresponding sides and angles are equal.

Given data:
AB = 6 cm, ∠B = 50°, ∠A = 70°

Step 1: Find ∠C in ΔABC.
Sum of angles in triangle = 180°
∠C = 180° - (∠A + ∠B) = 180° - (70° + 50°) = 60°

Step 2: Since ΔPQR ≅ ΔABC, corresponding angles and sides match:
- ∠A corresponds to ∠P = 70°
- ∠B corresponds to ∠Q = 50°
- ∠C corresponds to ∠R = 60°

Step 3: Corresponding sides:
- AB corresponds to PQ
- BC corresponds to QR
- CA corresponds to RP

Since AB = 6 cm, PQ = 6 cm.

Therefore, QP = 6 cm and ∠R = 60° is true.

Hence, option 4 is correct.

Answer

Answer

Answer