Difference between revisions of "Cyclic quadrilateral"
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| + | A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle. | ||
| − | + | ===Objectives=== | |
| − | + | Understanding cyclic quadrilaterals | |
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| − | + | Relation between angles of a cyclic quadrilateral. | |
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| − | = | + | ===Estimated Time=== |
| − | + | 10 minutes | |
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| − | = | + | ===Prerequisites/Instructions, prior preparations, if any=== |
| − | == | + | Circle and quadrilaterals should have been introduced. |
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| − | = | + | ===Materials/ Resources needed=== |
| + | Digital : Laptop, geogebra file, projector and a pointer. | ||
| − | + | Geogebra file: [https://ggbm.at/jdxxnrmb Cyclic quadrilateral.ggb] | |
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| − | + | {{Geogebra|jdxxnrmb}} | |
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| − | + | ===Process (How to do the activity)=== | |
| − | + | <span></span><span></span> | |
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# The teacher can recall the concept of a circle, quadrilateral, circumcircle. | # The teacher can recall the concept of a circle, quadrilateral, circumcircle. | ||
# Can explain a cyclic quadrilateral and show the geogebra applet. | # Can explain a cyclic quadrilateral and show the geogebra applet. | ||
# Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles. | # Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles. | ||
| − | + | * Developmental Questions: | |
# What two figures do you see in the figure ? | # What two figures do you see in the figure ? | ||
# Name the vertices of the quadrilateral. | # Name the vertices of the quadrilateral. | ||
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*Question Corner | *Question Corner | ||
# Can all quadrilaterals be cyclic ? | # Can all quadrilaterals be cyclic ? | ||
| − | # What are the necessary conditions for a quadrilateral to be cyclic ? | + | # What are the necessary conditions for a quadrilateral to be cyclic ? <span></span><span></span> |
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| − | + | [[Category:Circles]] | |
Latest revision as of 11:01, 31 October 2019
A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.
Objectives
Understanding cyclic quadrilaterals
Relation between angles of a cyclic quadrilateral.
Estimated Time
10 minutes
Prerequisites/Instructions, prior preparations, if any
Circle and quadrilaterals should have been introduced.
Materials/ Resources needed
Digital : Laptop, geogebra file, projector and a pointer.
Geogebra file: Cyclic quadrilateral.ggb
Download this geogebra file from this link.
Process (How to do the activity)
- The teacher can recall the concept of a circle, quadrilateral, circumcircle.
- Can explain a cyclic quadrilateral and show the geogebra applet.
- Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.
- Developmental Questions:
- What two figures do you see in the figure ?
- Name the vertices of the quadrilateral.
- Where are all the 4 vertices situated ?
- Name the opposite interior angles of the quadrilateral.
- What do you observe about them.
- Evaluation:
- Compare the cyclic quadrilateral to circumcircle.
- Question Corner
- Can all quadrilaterals be cyclic ?
- What are the necessary conditions for a quadrilateral to be cyclic ?