cyclic quadrilateral

AIM:
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".

Material Required:
coloured paper, pair if scissors, sketch pen, carbon paper, geometry box

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

cyclic quadrilateral properties