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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