Question

The pair of triangles below have two corresponding parts marked as congruent. What additional information is needed for a AAS congruence correspondence?A. ∠A≅∠MB. DA⎯⎯⎯⎯⎯⎯⎯⎯≅MO⎯⎯⎯⎯⎯⎯⎯⎯⎯C. ∠A≅∠OD. ∠O≅∠N

Answer 1

For the congruence of both triangles based on the AAS congruence theorem, it is required to have the additional information that: C. ∠A ≅ ∠O.

What is the AAS congruence Theorem?

The Angle-Angle-Side (AAS) congruence criterion assert that when two triangles share two congruent angles and a side adjacent to only one of these equal angles, the triangles are considered congruent to each other.

In the image shown, we see that:

DN ≅ TM [one pair of corresponding congruent sides]

∠D ≅ ∠T [one pair of corresponding congruent angles]

Therefore, for both triangles to be congruent by AAS congruence theorem, the additional information needed is: C. ∠A ≅ ∠O.

Answer 2

Step 1

Given; The pair of triangles below have two corresponding parts marked as congruent. What additional information is needed for an AAS congruence correspondence?

A. ∠A≅∠M

B. DA⎯⎯⎯⎯⎯⎯⎯⎯≅MO⎯⎯⎯⎯⎯⎯⎯⎯⎯

C. ∠A≅∠O

Step 2

AAS postulate means two angles and a side not included between them.

For these triangles it is given that;

`\begin{gathered} m\angle D\cong m\angle T \\ DN\cong TN \end{gathered}`

So we need one more angle for the postulate to be complete but this angle must not come in such a way that the congruent side is included in between thus;

`m\angle A\cong m\angle O\text{ is what is required}`

Answer;

`\angle A\cong\angle O`