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→Activity No #1.Both pairs of opposite angles of a cyclic quadrilateral are supplementary
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===
===Activity No #1.Both pairs of opposite angles of a cyclic quadrilateral are supplementary ===
===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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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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*Estimated Time
*Estimated Time :40 minutes
*Materials/ Resources needed
*Materials/ Resources needed:
Coloured paper, pair if scissors, sketch pen, carbon paper, geometry box
*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any
*Multimedia resources
*Multimedia resources
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets
*Process/ Developmental Questions
*Process:
# Draw a circle of any radius on a coloured paper and cut it.
# Paste the circle cut out on a rectangular sheet of paper.
# By paper folding get chords AB, BC, CD and DA in order.
# Draw AB, BC, CD & DA. A cyclic quadrilateral ABCD is obtained.
# Make a replica of cyclic quadrilateral ABCD using carbon paper.
# Cut the replica into 4 parts such that each part contains one angle .
# Draw a straight line on a paper.
# Place angle BAD and angle BCD adjacent to each other on the straight line.Write the observation.
# Place angle ABC and angle ADC adjacent to each other on the straight line . Write the observation.
# Produce AB to form a ray AE such that exterior angle CBE is formed.
# 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.
*Developmental Questions;
*Evaluation
*Evaluation
*Question Corner
*Question Corner
