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. (overline{de}congoverline{op}) reason: given (overline{dc}congoverline{rp}) reason: given (angle ocongangle e) reason: given

Explanation:

Step1: Identify congruence criteria

We have two right - angled triangles $\triangle DEC$ and $\triangle ROP$. We are given that $DE\cong OP$ (one pair of legs are equal) and $DC\cong RP$ (the hypotenuses are equal).

Step2: Apply HL (Hypotenuse - Leg) congruence theorem

In right - angled triangles, if the hypotenuse and one leg of one right - angled triangle are congruent to the hypotenuse and one leg of another right - angled triangle, then the two right - angled triangles are congruent. Since $\triangle DEC$ and $\triangle ROP$ are right - angled triangles with $DC\cong RP$ (hypotenuses) and $DE\cong OP$ (legs), by the HL congruence theorem, $\triangle DEC\cong\triangle ROP$.

Answer:

The triangles are necessarily congruent.