Question

Prove that two opposite arcs formed between two parallel chords of a circle are
congruent.
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Answer 1

Two opposite arcs formed between two parallel chords of a circle are congruent.

Step-by-step explanation:

Let say AB ║ CD  are chord

Now if we join BC

Then ∠ABC = ∠BCD  ( alternate angles)

Angle subtended by arc AC  = 2 ∠ABC

Angle subtended by arc BD  = 2 ∠BCD

∠ABC = ∠BCD

=> Angle subtended by arc AC  = Angle subtended by arc BD

Hence two opposite arcs formed between two parallel chords of a circle are congruent.