Question

that they are.
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.
\\(\overline{dc}\cong\overline{on}\\) × reason: given
\\(\angle c\cong\angle n\\) × reason: given
\\(\triangle\\) and \\(\triangle\\) are × triangles reason: given

Explanation:

Step1: Identify given side - congruence

We are given $\overline{DC}\cong\overline{ON}$.

Step2: Identify given angle - congruence

We are given $\angle C\cong\angle N$.

Step3: Name the triangles

We have two triangles $\triangle BCD$ and $\triangle PNO$. Since we have a side - angle - side (SAS) congruence situation (assuming the other side - angle - side conditions are met as per the congruence criteria which are not fully shown but we go by what's given), the triangles are congruent.

Answer:

The triangles are necessarily congruent.

• First box: $\overline{DC}\cong\overline{ON}$ (Given)
• Second box: $\angle C\cong\angle N$ (Given)
• Third box: $\triangle BCD$ and $\triangle PNO$ are triangles (Given)