Circle Theorem: Angles in the Same Segment Are Equal
(KS3, Year 8)

The Lesson

All triangles drawn from a chord in a circle make the same angle at the circumference.

How to Use the Circle Theorem where the Angles in the Same Segment Are Equal

Question

What is the angle θ in the circle below?

Step-by-Step:

1

The angles subtended by the chord at the circumference of the circle are equal.
θ = 40°

Answer:

The angle θ is 40°.

Lesson Slides

The slider below shows a real example of the circle theorem where the angles in the same segment are equal. Open the slider in a new tab

Useful Definitions

A semicircle is half a circle. A chord is a line whose endpoints lie on the circle.

A segment is a region, not containing the center, bounded by a chord and an arc lying between the chord's endpoints.

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See Also

What is a triangle? What is an angle? What is a circle? What are the circle theorems?