determine whether the triangles are similar by angle-angle similarity.\nare the two triangles similar by…

Explanation:

Step1: Identify the shared angle

Both triangles $\triangle LQP$ and $\triangle LMN$ share the vertex $L$, so $\angle QLP \cong \angle MLN$.

Step2: Identify parallel lines and corresponding angles

The arrows indicate that segment $QP$ is parallel to segment $MN$ ($QP \parallel MN$).

Step3: Apply the Corresponding Angles Postulate

Since $QP \parallel MN$, the corresponding angles $\angle LQP$ and $\angle LMN$ are congruent.

Step4: Verify Angle-Angle (AA) Similarity

Two pairs of corresponding angles are congruent ($\angle L \cong \angle L$ and $\angle LQP \cong \angle LMN$), satisfying the AA Similarity Postulate.

Answer:

Yes