Question

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

Explanation:

Step1: Identify congruent parts

We see that $\overline{CD}\cong\overline{NO}$, $\overline{DB}\cong\overline{OP}$, and $\angle CDB\cong\angle NOP$ (by the markings on the triangles).

Step2: Apply 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, the two triangles are congruent. Here, in $\triangle CDB$ and $\triangle NOP$, we have two pairs of congruent sides and the included angles are congruent. So, $\triangle CDB\cong\triangle NOP$.

Answer:

The two triangles are congruent by the SAS congruence criterion.