Question

are necessarily congruent.
in the first three boxes, choose a statement format from the dropdown menu. you will then be able to use letters to match the diagram for this problem.

≅ on × ∠ c ≅ ∠ n × △ bcd and △ pno are ×
reason: given reason: given reason: given

△nop≅△dcb

Explanation:

Step1: Identify given side congruence

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

Step2: Identify given angle congruence

$\angle C\cong\angle N$ (Given)

Step3: Consider required additional congruence

We need $\overline{CD}\cong\overline{NP}$ for SAS

Step4: Apply congruence postulate

If all three conditions are met, $\triangle NOP\cong\triangle DCB$ by SAS

Answer:

We are given two triangles $\triangle DCB$ and $\triangle PNO$. If we assume we have the following congruence - side $\overline{CB}\cong\overline{NO}$ (given), angle $\angle C\cong\angle N$ (given), and we know that $\triangle DCB$ and $\triangle PNO$ are triangles (given). To prove $\triangle NOP\cong\triangle DCB$, we can use the Side - Angle - Side (SAS) congruence criterion if we have another pair of corresponding sides equal. However, from the information provided, we can complete the proof steps as follows:

1. If we assume $\overline{CB}\cong\overline{NO}$ (Given)
2. $\angle C\cong\angle N$ (Given)
3. If we assume $\overline{CD}\cong\overline{NP}$ (Missing information to be given for a full proof by SAS)
4. Then $\triangle NOP\cong\triangle DCB$ by the SAS (Side - Angle - Side) congruence postulate.