Cyclic quadrilateral

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Concept #1. What is a Cyclic quadrilateral ?

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Concept #2. Theorems

Notes for teachers

===Activity No #1.By paper folding, cutting and pasting verify that 1) "The sum of interior opposite angles of cyclic quadrilateral is 180 degrees". 2) "In a cyclic quadrilateral the exterior angle is equal to interior opposite angle". ===

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• Estimated Time :40 minutes
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Coloured paper, pair if scissors, sketch pen, carbon paper, geometry box

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1. Draw a circle of any radius on a coloured paper and cut it.
2. Paste the circle cut out on a rectangular sheet of paper.
3. By paper folding get chords AB, BC, CD and DA in order.
4. Draw AB, BC, CD & DA. A cyclic quadrilateral ABCD is obtained.
5. Make a replica of cyclic quadrilateral ABCD using carbon paper.
6. Cut the replica into 4 parts such that each part contains one angle .
7. Draw a straight line on a paper.
8. Place angle BAD and angle BCD adjacent to each other on the straight line.Write the observation.
9. Place angle ABC and angle ADC adjacent to each other on the straight line . Write the observation.
10. Produce AB to form a ray AE such that exterior angle CBE is formed.
11. Make a replica of angle ADC and place it on angle CBE . Write the observation.

Observations : 1) angle BAD and angle BCD , when placed adjacent to each other on a straight line, completely cover the straight angle. This means their sum is 180 degrees. 2) angle ABC and angle ADC , when placed adjacent to each other on a straight line, completely cover the straight angle. This means their sum is 180 degrees. 3) The replica of angle ADC completely covers angle CBE. RESULT: a)The sum of either pair of opposite angle of a cyclic quadrilateral is 180 degrees.

b)In a cyclic quadrilateral, the exterior angle is equal to interior opposite angle.

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Activity No # 2. When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle

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Activity No #3. Suppose a quadrilateral is such that the sum of two opposite angles is a straight angle, then the quadrilateral is a cyclic quadrilteral.

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