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→Concept #1. What is a Cyclic quadrilateral ?
= Teaching Outlines =
= Teaching Outlines =
==Concept #1. What is a Cyclic quadrilateral ?==
==Concept # 1. Cyclic quadrilateral==
===Learning objectives===
# A quadrilateral ABCD is called cyclic if all of its four vertices 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.
===Notes for teachers===
===Activity#1 Cyclic quadrilateral ===
*Estimated Time 10 minutes
*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
*Prerequisites/Instructions, if any
# The students should know a circle and its parts.
# They should know that a quadrilateral is a 4 sided closed figure.
*Multimedia resources : Laptop
*Website interactives/ links/ / Geogebra Applets
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*Process:
# 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
# Name this special quadrilateral.
===Activity No # 2.Properties of a Cyclic quadrilateral===
*Estimated Time: 45 minutes
*Materials/ Resources needed
coloured paper, pair if scissors, sketch pen, carbon paper, geometry box
*Prerequisites/Instructions, if any
# The students should know a circle and a quadrilateral.
# They should know that in a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
# In a cyclic quadrilateral the exterior angle is equal to interior opposite angle
*Multimedia resources
*Website interactives/ links/ / Geogebra Applets
This activity has been taken from the website http://mykhmsmathclass.blogspot.in/2007/11/class-ix-activity-16.html
*Process:
Note: Refer the above geogebra file to understand the below mentioned labelling.
# Draw a circle of any radius on a coloured paper and cut it.
# Paste the circle cut out on a rectangular sheet of paper.
# By paper folding get chords AB, BC, CD and DA in order.
# Draw AB, BC, CD & DA. A cyclic quadrilateral ABCD is obtained.
# Make a replica of cyclic quadrilateral ABCD using carbon paper.
# Cut the replica into 4 parts such that each part contains one angle .
# Draw a straight line on a paper.
# Place angle BAD and angle BCD adjacent to each other on the straight line.Write the observation.
# Place angle ABC and angle ADC adjacent to each other on the straight line . Write the observation.
# Produce AB to form a ray AE such that exterior angle CBE is formed.
# Make a replica of angle ADC and place it on angle CBE . Write the observation.
Developmental Questions:
# How do you take radius ?
# What is the circumference ?
# What is a chord ?
# What is a quadrilateral ?
# Where are all four vertices of a quadrilateral located ?
# What part are we trying to cut and compare ?
# What can you infer ?
*Evaluation:
# Angle BAD and angle BCD, when placed adjacent to each other on a straight line, completely cover the straight angle.What does this mean ?
# Angle ABC and angle ADC, when placed adjacent to each other on a straight line, completely cover the straight angle.What can you conclude ?
# Compare angle ADC with angle CBE.
*Question Corner:
Name the two properties of cyclic quarilaterals.
==Concept #==
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===