Question

determine if the two triangles are necessarily congruent. if so, fill in a flowchart proof to prove that they are.
the triangles necessarily congruent.
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Identify given congruent parts

From the diagram:
$\angle Z = \angle L$, $ZY = ML$, $\angle Y = \angle M$

Step2: Match congruence criterion

The ASA (Angle-Side-Angle) congruence rule states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. Here, the side $ZY=ML$ is included between the two pairs of congruent angles.

Step3: Conclude triangle congruence

By ASA, $\triangle ZAY \cong \triangle LKM$

Answer:

The triangles are necessarily congruent.

Flowchart proof steps (in order):

1. Given: $\angle Z \cong \angle L$
2. Given: $\overline{ZY} \cong \overline{ML}$
3. Given: $\angle Y \cong \angle M$
4. By ASA Congruence Criterion: $\triangle ZAY \cong \triangle LKM$