Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.

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.