What additional piece of information would you need to be able to state that AK LM = AMNK by the SSS Congruence

Question

Theorem?
(1 point)
O KL~LM
• KM-KN

Answer 1

In order to apply the Side-Side-Side (SSS) Congruence Theorem and state that triangle AKL is congruent to triangle AMN, you need to know that all three pairs of corresponding sides are equal in length.

From the options given:

1. KL ~ LM suggests that KL is proportional to LM, but to apply SSS, we need equality, not just proportionality.

2. KM = KN directly states that the lengths of segments KM and KN are equal.

To confirm that AKL is congruent to AMN using the SSS Congruence Theorem, you would need to know that one more pair of sides is equal in length.

Therefore, the correct additional piece of information you would need is:

• KM = KN

This ensures that you can demonstrate that all three corresponding sides of triangles AKL and AMN are equal in length, thereby confirming their congruence by the SSS theorem.