Question

determine if the triangles are similar. if so, state the postulate or theorem and write the similarity statement.

Explanation:

Step1: Identify equal angles

We see that $\angle A=\angle D = 61^{\circ}$. Also, $\angle ACB$ and $\angle DCE$ are vertical - angles, so $\angle ACB=\angle DCE$.

Step2: Apply similarity theorem

By the Angle - Angle (AA) Similarity Theorem, if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.

Step3: Write similarity statement

The similarity statement is $\triangle ABC\sim\triangle DEC$.

Answer:

The triangles are similar by the AA Similarity Theorem. The similarity statement is $\triangle ABC\sim\triangle DEC$.