Difference between revisions of "A Kite and its properties"

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=   A Kite and its properties =
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= Concept Map =
 
[[File:kite.mm|flash]]
 
 
 
= Textbook =
 
To add textbook links, please follow these instructions to:
 
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
 
 
 
=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===
 
===Learning objectives===
 
# A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent.
 
# A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent.
Line 84: Line 50:
 
*Question Corner
 
*Question Corner
 
# Compare kite with other quadrilaterals and make a list of similarities and differences between them.
 
# Compare kite with other quadrilaterals and make a list of similarities and differences between them.
 
===Activity No # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*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===
 
# 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 <math>(1/2) (product  of  its  diagnols)</math>
 
 
===Notes for teachers===
 
===Activity No # 1. Deriving formula for area of a kite===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*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 # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
 
==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. ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*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
 
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*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 # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
 
= Hints for difficult problems =
 
 
= Project Ideas =
 
 
= Math Fun =
 
 
'''Usage'''
 
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 

Revision as of 11:23, 30 May 2019

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.

Kite.jpeg


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

  • 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.

Kite 1.jpeg Kite 2.jpeg Kite 3.jpeg Kite 4.jpeg


  • 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.