A Kite and its properties

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Additional Information

Useful websites

1. http://www.transum.org/software/Fun_Maths/kite. This website has good description and activities about kites.

Teaching Outlines

Concept # 1. A Kite and its properties

Learning objectives

1. A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent.
2. The two pairs of congruent sides meet at two different points.
3. A kite can also be described as a quadrilateral with an axis of symmetry along one of its diagonals.
4. Kites have a couple of properties that will help us identify them from other quadrilaterals.

• The diagonals of a kite meet at a right angle.
  
• Kites have exactly one pair of opposite angles that are congruent.
  
• Diagnols intersect at right angles.

<K = <M. This is the only pair of congruent angles because <J and <L have different measures.

Notes for teachers

Source : http://www.ask.com/question/what-is-a-kite-in-geometry
Summary :

1. A kite is sometimes also known as a deltoid.
2. A kite, may be either convex or concave, but the word "kite" is often restricted to the convex variety. A concave kite is sometimes called a "dart" or "arrowhead".

Activity No # 1. Paper kite

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• Estimated Time: 30 minutes.
• Materials/ Resources needed :

1. A4 sheet of paper.

• Prerequisites/Instructions, if any

1. Neat paper folding skills.
2. Ability to follow instructions.

• Multimedia resources
• Website interactives/ links/ / Geogebra Applets

This activity has been taken from the website : http://www.transum.org/software/Fun_Maths/kite/

• Process:

1. Fold an A4 sheet of paper as shown in the figures to make a kite.

• Developmental Questions:

1. Which is the figure formed ?
2. What is special about this quadrilateral ?
3. How many sides does a kite have ?
4. Are all sides equal ?
5. Mark the diagnols ? What do you notice about them ?

• Evaluation:

1. Were the students able dto recognise the properties of a kite.

• Question Corner

1. Compare kite with other quadrilaterals and make a list of similarities and differences between them.

Activity No #

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• Estimated Time
• Materials/ Resources needed
• Prerequisites/Instructions, if any
• Multimedia resources
• Website interactives/ links/ / Geogebra Applets
• Process/ Developmental Questions
• Evaluation
• Question Corner

Concept #2. Measurements in a kite

Learning objectives

1. A kite has two pairs of congruent sides.
2. Its diagnols intersect at right angles.
3. The sum of its four sides would be its perimetre.
4. Its area is given by the formula $(1/2)(productofitsdiagnols)$

Activity No # 1. Deriving formula for area of a kite

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• Estimated Time : 30 minutes.
• Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
• Prerequisites/Instructions, if any

1. Basics of a triangle and kite should have been done.

• Multimedia resources: Laptop
• Website interactives/ links/ / Geogebra Applets
• Process:

1. The teacher can project the geogebra file on kite.
2. Show them that a kite is made of two isosceles traingles.
3. Sum of areas of these two triangles would be the area of the kite.

• Developmental Questions

1. What is a kite /
2. What are the properties of a kite.
3. What other figures can you see in a kite ?
4. What types of triangles are these ?
5. Identify the two isosceles triangles ?
6. What is the formula to find the area of a triangle ?

• Evaluation:

1. Choosing which two traingles out of the 8 visible types would be easy to deduce the area of kite ?

• Question Corner:

1. Recall the two formulae that you know to find the area of a triangle.

Activity No #

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• Estimated Time
• Materials/ Resources needed
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• Multimedia resources
• Website interactives/ links/ / Geogebra Applets
• Process/ Developmental Questions
• Evaluation
• Question Corner

Concept # 3. Construction of a kite

Learning objectives

1. Learn steps for constructing a kite with given measures.

Activity No # 1. Construction of a kite.

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• Estimated Time : 20 minutes.
• Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
• Prerequisites/Instructions, if any:

1. Students should have prior knowledge about a kite and its properties.
2. They should know a perpendicular line and its construction.
3. They should know to construct a line segment of given length by constructing arcs.

• Multimedia resources: Laptop
• Website interactives/ links/ / Geogebra Applets

• Process:

1. The teacher can initially have a recaptualation of the concept of a kite and its properties.
2. Give them measures say, "Construct a kite which has its congruent sides as 4 cm and 6 cm a pair with one of its diagnols measuring 5cm.
3. Can project the geogebra file and explain the steps of construction for the given measures.

• Draw a rough small kite labelling with the given measures.
• Begin with drawing a line segment, the diagnol of a given measure, here 5 cm. label it as AB.
• Draw a perpendicular bisector to this line segment AB.
• With A as centre construct an arc with 4cm as radius. Mark the intersecting point of arc with the perpendicular bisector as D. Join AD.
• With B as centre construct another arc with the same radius 4cm. You get the same point D as point of intersection .
• Join AD and BD which would measure 4cm each and would become one pair of congruent sides of the kite.
• Similarly draw arcs on the other side taking radius as 6cm to get other pair of congruent sides.
• ADBE would be the specified kite.

• Developmental Questions:

1. What are the properties of a kite ?
2. What measures are given for constructing a kite ?
3. By which given measure can we begin the kite construction ?
4. What is the angle between the two diagnols in a kite ?
5. For what purpose are we drawing the perpendicular bisector ?
6. What is the purpose of drawing an arc ?
7. What should be measure of the radius of the arc ?
8. Why should AD and BD be same ?

• Evaluation:

1. Check if the constructed kite satisfies all of its properties.

• Question Corner:

1. Can you think of any other method of kite construction for the given measures ?

Activity No #

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• Evaluation
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