GCSE Maths (AQA)

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Opposite Angles in a Quadrilateral

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Geometry and Measures Properties and Constructions

Opposite Angles in a Quadrilateral

4:06 Even More Circle Theorems
Spec G10
Previous Front & Side Elevations Next Alternate Segment Theorem
  • A cyclic quadrilateral is a quadrilateral with all four vertices lying on the circumference of a circle.
  • The opposite angles of a cyclic quadrilateral add up to 180 degrees.
  • The angles at the circumference subtended by the same arc are equal.
  • To prove the circle theorem, draw in the diagonals of the quadrilateral and split one of the angles.
  • Use the circle theorem to find two equivalent angles in the diagram.
  • Find an expression for the opposite angle in the quadrilateral.
  • Determine that the sum of the opposite angles will be 180 degrees.
  • This proves the circle theorem that opposite angles in a cyclic quadrilateral add up to 180 degrees.

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