Question

Identify the correct explanation and the similarity statement for the similar triangles.

Answer 1

Answer:

Option B

Step-by-step explanation:

From the picture attached,

In ΔABC,

m∠B = m∠C = 75° [Isosceles triangles]

By applying triangle sum theorem,

m∠A + m∠B + mC = 180°

m∠A + 75° + 75° = 180°

m∠A = 180° - 150°

m∠A = 30°

In triangle PQR,

m∠P = m∠Q [Isosceles triangle]

By applying triangle sum theorem,

m∠P + m∠Q + m∠R = 180°

2(m∠P) + 30° = 180°

m∠P = 75°

m∠P = m∠Q = 75°

In ΔABC and ΔRPQ,

m∠B ≅ m∠Q [Given]

m∠C ≅ m∠R [Given]

Therefore, by AA property of similarity of two triangles, both the triangles will be similar.

ΔABC ~ ΔRPQ

Option B will be the answer.