Question

if ∠m ≅ ∠y, is δlmn ≅ δxyz?

Explanation:

Step1: Identify given congruences

We have two sides and the included angle? Wait, no, let's check the markings. In $\triangle LMN$ and $\triangle XYZ$, we see that $LM$ and $XY$ have one tick mark (so $LM \cong XY$), $MN$ and $YZ$ have two tick marks (so $MN \cong YZ$), and we are given $\angle M \cong \angle Y$.

Step2: Apply SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, $LM \cong XY$, $\angle M \cong \angle Y$, and $MN \cong YZ$. The angle $\angle M$ is included between $LM$ and $MN$, and $\angle Y$ is included between $XY$ and $YZ$. So by SAS, $\triangle LMN \cong \triangle XYZ$.

Answer:

Yes