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.

reason: given

reason: given

reason: given

△mno≅△cba
reason: sas

Explanation:

Step1: Identify congruent sides

From the diagram, we can see that $\overline{AB}\cong\overline{ON}$, $\overline{BC}\cong\overline{NM}$, $\overline{AC}\cong\overline{OM}$ are given.

Step2: Apply congruence criterion

Since we have two - sides and the included - angle of one triangle congruent to two - sides and the included - angle of the other triangle (SAS - Side - Angle - Side congruence criterion), we can prove $\triangle MNO\cong\triangle CBA$.

Answer:

First box: $\overline{AB}\cong\overline{ON}$, Reason: GIVEN
Second box: $\overline{BC}\cong\overline{NM}$, Reason: GIVEN
Third box: $\overline{AC}\cong\overline{OM}$, Reason: GIVEN
Bottom box: $\triangle MNO\cong\triangle CBA$, Reason: SAS