# Circle Theorem: Angles in the Same Segment Are Equal (Mathematics Lesson)

# Circle Theorem: Angles in the Same Segment Are Equal

All triangles drawn from a chord in a circle make the same angle at the circumference.# How to Use the Circle Theorem that the Angles in the Same Segment Are Equal

**Question:**What is the angle θ in the circle below?

The angles subtended by the chord at the circumference of the circle are equal.

θ = 40°

# A Real Example of How to Use the Circle Theorem that the Angles in the Same Segment Are Equal

The slider below shows a real example of the circle theorem that the angles in the same segment are equal:##### Curriculum

##### Interactive Test

**show**

##### Note

# USEFUL DEFINITIONS

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.