Question

△uvw and △xyz are shown below. which statement is true? △uvw is similar to △xyz. △uvw is not similar to △xyz. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Determine the type of triangles

$\triangle UVW$ is an isosceles triangle (two sides are equal). $\triangle XYZ$ is an isosceles triangle (two sides are equal) with vertex angle $120^{\circ}$.

Step2: Calculate the base angles of $\triangle XYZ$

Using the angle - sum property of a triangle ($\angle X+\angle Y+\angle Z = 180^{\circ}$). Let $\angle X=\angle Z$. Then $2\angle X+120^{\circ}=180^{\circ}$, so $2\angle X = 60^{\circ}$, and $\angle X=\angle Z = 30^{\circ}$.
For $\triangle UVW$, since it is isosceles, if we assume the non - equal angle (vertex angle) is not given. But for similarity, we need either AA (angle - angle), SAS (side - angle - side) similarity etc.
The base angles of $\triangle UVW$ (if it were an isosceles triangle with equal sides) would be $\frac{180^{\circ}-\text{vertex angle}}{2}$. Since we don't know the measure of any angle of $\triangle UVW$, we cannot establish a similarity (no AA criterion can be applied as we don't have angle measures for $\triangle UVW$ to match with $\triangle XYZ$ angles).

Answer:

$\triangle UVW$ is not similar to $\triangle XYZ$.