Question

write a triangle congruence flowchart proof to prove that angle a is congruent to angle c. name: ella smith date: 10/1/25 period: 1 unit 2: homework 2 due: 10/9 or 10/10 grading rubric emerging i can start some problems developing i can attempt most essential problems nearing i can attempt all essential problems with thinking shown proficient i can attempt all problems with thinking shown elite level i can do all problems correctly with thinking shown

Explanation:

Step1: Identify congruent - side information

We see that in triangles $\triangle ABD$ and $\triangle CDB$, $AB = CD$ and $AD = CB$ (marked with single - cross and double - cross respectively). Also, $BD$ is common to both triangles.

Step2: Apply SSS (Side - Side - Side) congruence criterion

By SSS congruence criterion, $\triangle ABD\cong\triangle CDB$ since $AB = CD$, $AD = CB$, and $BD=BD$.

Step3: Use corresponding parts of congruent triangles

Since $\triangle ABD\cong\triangle CDB$, corresponding angles are congruent. So, $\angle A\cong\angle C$ (corresponding angles of congruent triangles $\triangle ABD$ and $\triangle CDB$).

Answer:

1. First box (left - hand side of flowchart): $AB = CD$
2. Second box (middle of flowchart): $AD = CB$
3. Third box (right - hand side of flowchart): $BD = BD$
4. Fourth box (below the three boxes): $\triangle ABD\cong\triangle CDB$ (by SSS)
5. Fifth box (bottom of flowchart): $\angle A\cong\angle C$ (corresponding parts of congruent triangles)