Theorems on cyclic quadrilaterals

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  1. Both pairs of opposite angles of a cyclic quadrilateral are supplementary.
  2. When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle.

Converse theorems:

  1. Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, them the quadrilateral is cyclic.
  2. If the exterior angle of a quadrilateral is equal to the interior opposite angle, then the quadrilateral is cyclic.

Estimated Time

40 minutes

Prerequisites/Instructions, prior preparations, if any

Laptop, geogebra file, projector and a pointer

Materials/ Resources needed

  1. A cyclic quadrilateral and its properties.
  2. The linear pair and exterior angle theorem.
  3. The circle theorem (Angle at centre = double the angle at the circumference)

This geogebra file was done by ITfC-Edu-Team.

Process (How to do the activity)

  • Process:
  1. The teacher can project the geogebra file and prove the theorems.
  • Developmental Questions:
  1. How many angles does a cyclic quadrilateral have ?
  2. Name the opposite angles of it.
  3. Name the minor arc.
  4. Recall the angle -arc theorem.
  5. What is the total angle at the centre of a circle ?
  6. Name the angles at the centre of the circle.
  7. What is the sum of those two angles ?
  8. How can you show that