Angles in the Same Segment

Circles & Segmentsvideo

Circles & segments

Circle Theorem: Angles in the same segment are equal

• Any two angles on the circumference of a circle that are formed from the same two points on the circumference are equal

  • These two angles are in the same segment of the circle

    • To see this, add the chord PQ below to split the circle into two segments

• To spot this circle theorem on a diagram

  • Find two points on the circumference that meet at a third point

  • See if there are any other pairs of lines from the same two original points that meet at a different point on the circumference

• When explaining this theorem in an exam you must use the keywords:

  • Angles in the same segment are equal

• Look out for a bowtie shape

  • The theorem works upside down, in that the angles at P and Q are also equal