Question

isosceles triangle abc is folded along bm with m chosen in such a way that it is the mid - point of side ac, the shortest side.
which pair of sides are congruent based on the definition of mid - point?
which pair of sides are congruent based on the reflexive property?
which pair of sides are congruent based on the definition of isosceles triangles?

Explanation:

Step1: Midpoint divides segment equally

Midpoint M of AC implies AM = MC.

Step2: Reflexive property (common side)

Side BM is congruent to itself (BM = BM).

Step3: Isosceles triangle congruent legs

Assuming ABC is isosceles with AB = BC, triangles ABM ≅ CBM by SSS.

Answer:

1. AM and MC
2. BM and BM
3. Triangles ABM and CBM