Given:
Triangle RQS and Triangle UVT
To find:
whether the triangles are similar or not.
Solution:
In triangle RQS,
Sum of all the angles of a triangle = 180°
m∠R + m∠Q + m∠S = 180°
m∠R + 85° + 35° = 180°
m∠R + 120° = 180°
Subtract 120° from both sides,
m∠R = 60°
In triangle VUT,
Sum of all the angles of a triangle = 180°
m∠V + m∠U + m∠T = 180°
m∠V + 65° + 35° = 180°
m∠V + 100° = 180°
Subtract 100° from both sides,
m∠V = 80°
If two triangles are similar then their angles are congruent.
In ΔRQS,
∠R= 60°, ∠Q= 85°, ∠S= 35°,
In ΔVUT,
∠V= 80°, ∠U= 65°, ∠T= 35°,
Here the angles are not congruent.
Therefore the triangles are not similar.