A Kite and its properties

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= Concept Map = flash

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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.

Reference Books
= Teaching Outlines =

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



Notes for teachers

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

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

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 $$1/2 x product of its diagnols $$

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
 * 1) They should know a kite and its properties.
 * 2) The students should know the concept of an area.
 * 3) They should know the formula to find the area of a triangle.
 * 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 #

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

Learning objectives

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

Activity No # 1. Construction of a kite.
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
 * 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 #

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

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= Math Fun =

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