If in congruent circles two arcs are equal, then their corresponding chords will be—

Let us take a circle with O as centre and radius r in which arc AB ≅ arc CD.

Construction:

Join OA, OB, OC and OD.

In ΔAOB and ΔCOD,

⇒ OA = OC [radii of same circle]

⇒OB = OD [radii of same circle]

⇒∠AOB = ∠COD [measure (arc AB) = measure (arc CD)]

By SAS congruency,

⇒ ΔAOB ≅ ΔCOD

By CPCT,

⇒ AB = CD

∴ In congruent circles, if two arcs are equal, then their corresponding chords will be equal.