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. type of statement reason: given type of statement reason: given type of statement reason: given △nop≅△dcb reason: select reason

Explanation:

Step1: Identify congruence - side markings

The side - side - side (SSS) congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In the diagram, we can see that the sides of $\triangle NOP$ and $\triangle DCB$ have corresponding equal - length markings.

Step2: Determine congruence

Since the three sides of $\triangle NOP$ are congruent to the three sides of $\triangle DCB$ (by the given side - length markings), we can conclude that $\triangle NOP\cong\triangle DCB$ by the SSS congruence postulate.

Answer:

The triangles are necessarily congruent. Reasons for the statements could be:

1. $NO = DC$ (Given, based on side - length markings)
2. $OP=CB$ (Given, based on side - length markings)
3. $NP = DB$ (Given, based on side - length markings)

And $\triangle NOP\cong\triangle DCB$ by SSS (Side - Side - Side) congruence postulate.