Given:
cm bisects ab
ac = bc

based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove the triangles congruent. if it is not possible to prove the triangles are congruent, choose "not possible".

sss
sas
asa
not possible

The correct option is 1, i.e., SSS.

Explanation:

It is given that in triangle ABC the line CM bisects AB. The side AC=BC. In triangle ACM and BCM,

AM = BM      (CM bisects AB)

CM=CM        (common side)

AC= BC         (given)

Since three sides of triangles are equal.

According to SSS rule of congruence theorem, two triangles are congruent if all the corresponding sides of the triangles are equal.

So by SSS rule of congruence theorem, we can conclude that the triangles  ACM and BCM are congruent.

The correct option is first, i.e., SSS rule.