Question

What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem? NL ≅ MP NK ≅ MQ AngleN ≅ AngleM AngleL ≅ AngleP.

Answer 1

No additional information is needed to prove that the triangles are congruent using the A-S-A congruence theorem.

Given,

We have $\Delta \rm LKN$ and $\Delta\rm PQM$ in which side NL is congruent to side MP, side NK is congruent to side MQ.

$\angle\rm N$ is congruent to $\angle\rm M$, $\angle\rm L$ is congruent to $\angle \rm P$.

A-S-A congruence rule

A-S-A congruence rule states that if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles are considered to be congruent.

Here in

$\Delta \rm LKN\ \rm and \ \Delta\rm PQM$,

$\angle\rm N=\angle\rm M$ ( given )$\rm NL=\rm PM$ ( given )

$\angle\rm L=\angle \rm P$ ( given )

So, by Angle-Side-Angle congruence rule,

$\Delta \rm LKN\ \cong \Delta\rm PQM$.

Thus, no more information is needed for the triangles to be congruent by A-S-A congruence theorem.

For more details on Congruence rule follow the link:

https://brainly.com/question/19258025