Cyclic Quadrilaterals
From Karnataka Open Educational Resources
Objectives
Understanding about cyclic Quadrilaterals
Being able to deduce that a quadrilateral is cyclic if and only if its opposite angles are supplementary
Estimated Time
30 minutes
Prerequisites/Instructions, prior preparations, if any
knowledge about vertices, segments, angles, circles, quadrilaterals and its types, supplementary angles
Materials/ Resources needed
Click here to open the file
Non-digital :paper, pencil, compass, ruler, protractor
Process (How to do the activity)
Download this geogebra file from this link.
Procedure:
- Draw a circle with centre O.
- Take any four points A, B, C, D on the circumference of the circles.
- Join AB, BC, CD, DA on the circles
- Identify the quadrilateral on the circle
- What you called for this type of quadrilaterals?
- What is cyclic quadrilaterals?
- Identify and measure the angles in the cyclic quadrilaterals?
- Identify pair of opposite angles in cyclic quadrilaterals?
- What is the sum of opposite angles of a cyclic quadrilateral ?what is your conclusion?
Sl no. | Quadrilateral | Angles | Pair of Opposite angles 1 | Pair of opposite angles 2 | Sum of opposite angles1 | Sum of opposite angles 2 | Conclusion | |||
1 | 2 | 3 | 4 | |||||||
1 |
Evaluation at the end of the activity
- If one of the angles of a cyclic quadrilateral is 30°, then what will the value of its opposite angle ?
- Find the value of angle D of a cyclic quadrilateral, if angle B is 60°?
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