**EQUAL ANGLES SUBTENDS CONGRUENT ARCS**

In a circle the angle subtended by the two arcs are equal , then these two arcs are called congruent.Watch Congruent Arcs Videos to learn more.

If two arcs of a circle are congruent , if the angles subtended by them at the centre are equal. If two central angles of a circle (or of congruent circles) are congruent, then their intercepted arcs are congruent.

Given: Two congruent arcs AB and CD.

To prove: ∠ AOB = ∠COD

Construction: Draw chords AB and CD.

Proof: The angle subtended by an arc at the centre is equal to the angle subtended by its corresponding chord at the centre.

In the given figure,

AB = CD (Chords corresponding to congruent arcs of a circle are equal)

∠AOB = ∠COD (Equal chords subtend equal angles at the centre)

Hence, the theorem is proved.

**Congruent Arcs Videos**

Useful for CBSE, ICSE, NCERT & International Students

Grade : 9

Subject : Maths

Lesson : Circles

Topic: Congruent Arcs Videos

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