Final answer:
To prove AC ≅ BC, one can utilize the Hypotenuse-Leg Congruence theorem by showing that triangles CAD and CBD are congruent, leading to AC and BC being congruent as corresponding parts of congruent triangles (CPCTC).
Step-by-step explanation:
The student's question involves proving that AC ≅ BC given that (M) is the midpoint of (AB), (CD perp AB), and that (∠ CAD) and (∠ CBD) are right angles. Assuming AD and BC are radii of a circle centered at C, AC equals to BC since radii of the same circle are congruent. By applying the properties of perpendicular bisectors and right angles, we can establish that triangles CAD and CBD are congruent by the Hypotenuse-Leg Congruence theorem (HL Congruence). Since CD is a common side to both triangles and AD = DB because M is the midpoint of AB, the two triangles are congruent. Therefore, AC must be congruent to BC as they are corresponding parts of congruent triangles (CPCTC)