Question

Given:

Answer 1

Answer: 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.

Answer 2

We can use the SSS congruence theorem to prove that the two triangles in the attached figure are congruent. The SSS or side-side-side theorem states that each side in the first triangle must have the same measurement or must be congruent on each of the opposite side of another triangle. In this problem, for the first triangle, we have sides AC, CM, AM while in the second triangle we have sides BC, CM, and BM. By SSS congruent theorem, we have the congruent side as below:
AC = BC
CM = CM
AM = BM 

The answer is SSS theorem.