Question

10
given:
\\( \angle l m a \cong \angle a m e \\)
\\( \overline{l m} \cong \overline{m e} \\)
\\( \triangle a m l \cong \triangle \\)__ by__

Explanation:

Step1: Identify the given congruent parts

We are given that $\angle LMA\cong\angle AME$ (angle), $\overline{LM}\cong\overline{ME}$ (side), and $\overline{AM}$ is common to both $\triangle AML$ and $\triangle AME$ (side).

Step2: Apply the congruence criterion

By the Side - Angle - Side ($SAS$) congruence criterion, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Here, in $\triangle AML$ and $\triangle AME$, we have two sides ($\overline{LM}\cong\overline{ME}$ and $\overline{AM}\cong\overline{AM}$) and the included angle ($\angle LMA\cong\angle AME$) congruent. So, $\triangle AML\cong\triangle AME$ by $SAS$.

Answer:

$\triangle AME$; $SAS$