Theorems on cyclic quadrilaterals
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- Both pairs of opposite angles of a cyclic quadrilateral are supplementary.
- When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle.
- Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, them the quadrilateral is cyclic.
- If the exterior angle of a quadrilateral is equal to the interior opposite angle, then the quadrilateral is cyclic.
Prerequisites/Instructions, prior preparations, if any
Laptop, geogebra file, projector and a pointer
Materials/ Resources needed
- A cyclic quadrilateral and its properties.
- The linear pair and exterior angle theorem.
- 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)
- The teacher can project the geogebra file and prove the theorems.
- Developmental Questions:
- How many angles does a cyclic quadrilateral have ?
- Name the opposite angles of it.
- Name the minor arc.
- Recall the angle -arc theorem.
- What is the total angle at the centre of a circle ?
- Name the angles at the centre of the circle.
- What is the sum of those two angles ?
- How can you show that