Difference between revisions of "Cyclic quadrilateral"
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| Line 68: | Line 68: | ||
===Learning objectives=== | ===Learning objectives=== | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
| − | ===Activity No #1. | + | ===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". === | ||
{| style="height:10px; float:right; align:center;" | {| style="height:10px; float:right; align:center;" | ||
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
|} | |} | ||
| − | *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 | + | *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 | ||
Revision as of 21:41, 16 December 2013
| Philosophy of Mathematics |
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Teaching Outlines
Concept #1. What is a Cyclic quadrilateral ?
Learning objectives
Notes for teachers
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Concept #2. Theorems
Learning objectives
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". ===
- Estimated Time :40 minutes
- Materials/ Resources needed:
Coloured paper, pair if scissors, sketch pen, carbon paper, geometry box
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- 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
- Question Corner
Activity No # 2. When one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
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.
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
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Math Fun
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