# Cyclic Quadrilaterals

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### Objectives

Understanding about cyclic Quadrilaterals

Being able to deduce that a quadrilateral is cyclic if and only if its opposite angles are supplementary

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:

1. Draw a circle with centre O.
2. Take any four points A, B, C, D on the circumference of the circles.
3. Join AB, BC, CD, DA on the circles
4. Identify the quadrilateral on the circle
5. What you called for this type of quadrilaterals?
6. What is cyclic quadrilaterals?
7. Identify and measure the angles in the cyclic quadrilaterals?
8. Identify pair of opposite angles in cyclic quadrilaterals?
9. What is the sum of opposite angles of a cyclic quadrilateral ?what is your conclusion?

### Evaluation at the end of the activity

1. If one of the angles of a cyclic quadrilateral is 30°, then what will the value of its opposite angle ?
2. Find the value of angle D of a cyclic quadrilateral, if angle B is 60°?

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