Question

Consider a circle with centre O and chords AB and CD.chord AB = Chord CD . Prove that arc AB = arc CD ​

Answer 1

see the steps of the proof below

Explanation:

You want to prove congruent chords AB and CD of circle O subtend congruent arcs AB and CD.

Proof

Statement . . . . Reason

1. AB ≅ CD; A, B, C, D lie on circle O . . . . given

2. OA ≅ OB ≅ OC ≅ OD . . . . definition of a circle

3. ∆OAB ≅ ∆OCD . . . . SSS congruence postulate

4. ∠AOB ≅ ∠COD . . . . CPCTC

5. arc AB ≅ arc CD . . . . definition of arc measure: same as central angle measure

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