In triangles PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Is △QPR ~ △TSM? Why
Solution:
Given, in the triangles PQR and MST,
∠P = 55°
∠Q = 25°
∠M = 100°
∠S = 25°
We have to find if the triangles QPR and TSM are similar.
We know that the sum of the interior angles of a triangle are always equal to 180°
In triangle PQR,
∠P + ∠Q + ∠R = 180°
55°+ 25°+ ∠R = 180°
80°+ ∠R = 180°
∠R = 180° - 80°
∠R = 100°
In triangle MST,
∠M + ∠S + ∠T = 180°
100° + 25° + ∠T = 180°
125° + ∠T = 180°
∠T = 180°-125°
∠T = 55°
Comparing triangles PQR and MST,
∠P = ∠T = 55°
∠Q = ∠S = 25°
∠R = ∠M = 100°
We know that similar triangles have congruent corresponding angles.
Therefore, △QPR ~ △TSM
✦ Try This: In triangles PQR and ABC, ∠P = 45°, ∠Q = 35°, ∠A = 80° and ∠S = 45°. Is △QPR ~ △ABC? Why
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 5
In triangles PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Is △QPR ~ △TSM? Why
Summary:
In triangles PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. △QPR ~ △TSM are similar as the corresponding angles are equal
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