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. cd ≅ no reason: given bd ≅ po reason: given △nop and △dcb are triangles reason: given △nop ≅ △dcb reason: sas

Explanation:

Step1: Identify given side - side equalities

We are given $\overline{CD}\cong\overline{NO}$ and $\overline{BD}\cong\overline{PO}$.

Step2: Identify included angle

The included angles $\angle D$ and $\angle O$ are equal (since $\triangle NOP$ and $\triangle DCB$ are given as related in a way that implies the included - angle equality).

Step3: 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. So, $\triangle NOP\cong\triangle DCB$.

Answer:

$\triangle NOP\cong\triangle DCB$ by SAS