Question

Given: m (MINOR ARC) AB = m (MINOR ARC) CD
PROVE: m AB = mCD

Answer 1

I can give you an idea, then you can write a two column proof.

Answer 2

The measure of a minor arc equals the measure of the central angle that subtends it.

Answer 3

That means since minor arcs AB and CD are congruent, that means central angles AOB and COB are congruent.

Answer 4

Then since you are dealing with a circle, all radii are congruent.
That means segments OA and OC are congruent and segments OB and OD are congruent.
Then BY SAS, triangles AOB and COD are congruent.
Finally by CPCTC, segments AB and CD are congruent.