Question

determine if the two triangles are necessarily congruent. if so, fill in a flowchart proof to prove that they are.

the triangles are necessarily congruent.
for each of the first three boxes, choose a statement format from the dropdown menu. you will then be able to change the letters to match the diagram for this problem.

Explanation:

Step1: Identify given congruent parts

From the diagram:

1. $\angle Z \cong \angle K$
2. $\overline{ZA} \cong \overline{KL}$
3. $\angle A \cong \angle L$

Step2: Match to 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 $\overline{ZA}/\overline{KL}$ is the included side between the two pairs of congruent angles.

Step3: Conclude triangle congruence

By the ASA congruence postulate, $\triangle YZA \cong \triangle MKL$.

Answer:

The triangles are necessarily congruent.

1. Statement 1: $\boldsymbol{\angle Z \cong \angle K}$ (Given)
2. Statement 2: $\boldsymbol{\overline{ZA} \cong \overline{KL}}$ (Given)
3. Statement 3: $\boldsymbol{\angle A \cong \angle L}$ (Given)
4. Conclusion: $\boldsymbol{\triangle YZA \cong \triangle MKL}$ (By ASA Congruence Postulate)