# A Kite and its properties

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Philosophy of Mathematics |

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# Concept Map

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# Textbook

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# Additional Information

## Useful websites

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

## Reference Books

# Teaching Outlines

## Concept # 1. A Kite and its properties

### Learning objectives

- A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent.
- The two pairs of congruent sides meet at two different points.
- A kite can also be described as a quadrilateral with an axis of symmetry along one of its diagonals.
- 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 :

- A kite is sometimes also known as a deltoid.
- 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

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

- A4 sheet of paper.

- Prerequisites/Instructions, if any

- Neat paper folding skills.
- 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:

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

- Developmental Questions:

- Which is the figure formed ?
- What is special about this quadrilateral ?
- How many sides does a kite have ?
- Are all sides equal ?
- Mark the diagnols ? What do you notice about them ?

- Evaluation:

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

- Question Corner

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

### Activity No #

- Estimated Time
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## Concept #2. Measurements in a kite

### Learning objectives

- A kite has two pairs of congruent sides.
- Its diagnols intersect at right angles.
- The sum of its four sides would be its perimetre.
- Its area is given by the formula

### Notes for teachers

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

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

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

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

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

- Developmental Questions

- What is a kite ?
- What are the properties of a kite.
- What other figures can you see in a kite ?
- What types of triangles are these ?
- Identify the two isosceles triangles ?
- What is the formula to find the area of a triangle ?

- Evaluation:

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

- Question Corner:

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

### Activity No #

- Estimated Time
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## Concept # 3. Construction of a kite

### Learning objectives

- Learn steps for constructing a kite with given measures.

### Notes for teachers

### Activity No # 1. Construction of a kite.

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

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

- Multimedia resources: Laptop
- Website interactives/ links/ / Geogebra Applets: This geogebra file has been done by ITfC-Edu-Team

- Process:

- The teacher can initially have a recaptualation of the concept of a kite and its properties.
- 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.
- 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:

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

- Evaluation:

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

- Question Corner:

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

### Activity No #

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