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 equal - side pairs

$\overline{CD}\cong\overline{NO}$ (Given)

Step2: Identify equal - side pairs

$\overline{BD}\cong\overline{PO}$ (Given)

Step3: Identify equal - angle pairs

$\angle CDB\cong\angle NOP$ (Given)

Step4: Determine congruence criterion

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

Answer:

First box: $\overline{CD}\cong\overline{NO}$; Second box: $\overline{BD}\cong\overline{PO}$; Third box: $\angle CDB\cong\angle NOP$; Reason for $\triangle NOP\cong\triangle DCB$: SAS