Question

Determine whether the triangles are similar. If so, write a similarity statement. answers:: A) The triangles are similar; ΔQRS ∼ ΔTUV. B) There isn't enough information to determine whether the triangles are similar. C) The triangles are not similar. D) The triangles are similar; ΔQRS ∼ ΔVUT.

Answer 1

C) The triangles are not similar

Explanation:

There are 3 triangle similarity theorems:

• If two of the angles are the same, the third angle is the same and the triangles are similar.
• If the three sides are in the same proportions, the triangles are similar.
• If two sides are in the same proportions and the included angle is the same, the triangles are similar.

We can find the all the angles of both triangles, so we can determine the similarity of these triangles only by first theorem

Angles of ΔQRS:

<Q = 63°

<R = 90°

<S = 180°-63°-90° = 27°

Angles of ΔTUV:

<T=180°-90°-25° = 65°

<U = 90°

<V = 25°

As none of the angles are same, triangles are not similar.