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

homesitemapgeometryangles in the same segment are equal
All triangles drawn from a chord in a circle make the same angle at the circumference.

## Question

What is the angle θ in the circle below?

## 1

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

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.

## 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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