Question

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. △nop≅△dcb

Explanation:

Step1: Identify congruent sides

From the diagram, we see that $\overline{NO}\cong\overline{DC}$ (given).

Step2: Identify another congruent side

We also have $\overline{OP}\cong\overline{CB}$ (given).

Step3: Identify congruent angle

And $\angle O\cong\angle C$ (given).

Step4: Apply congruence criterion

By the Side - Angle - Side (SAS) congruence criterion, since we have two pairs of congruent sides and the included angles are congruent, $\triangle NOP\cong\triangle DCB$.

Answer:

$\triangle NOP\cong\triangle DCB$ by SAS (Side - Angle - Side)