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From Karnataka Open Educational Resources
The longest chord passes through the centre of the circle (view source)
Revision as of 04:45, 3 November 2013
, 04:45, 3 November 2013no edit summary
==Reference Books==
==Reference Books==
= Teaching Outlines =
= Teaching Outlines
Chord and its related theorems
==Concept #1 CHORD==
==Concept #1 CHORD==
===Learning objectives===
===Learning objectives===
The students should be able to:<br>
The students should be able to:<br>
#Recall the meaning of circle and chord.<br>
#State Properties of chord.<br>
# By studying the theorems related to chords, the students should know that a chord in a circle is an important concept .
# They should be able to relate chord properties to find unknown measures in a circle.
# They should be able to apply chord properties for proof of further theorems in circles.
===Notes for teachers===
===Notes for teachers===
The teacher should clarify the meaning of chord and circle to the students
A chord is a straight line joining 2 points on the circumference of a circle. Chords within a circle can be related many ways. The theorems that involve chords of a circle are :
Perpendicular bisector of a chord passes through the center of a circle.
Congruent chords are equidistant from the center of a circle.
If two chords in a circle are congruent, then their intercepted arcs are congruent.
If two chords in a circle are congruent, then they determine two central angles that are congruent.
===Activity No 1 Construction of chord ===
===Activity No 1 ===
{| style="height:10px; float:right; align:center;"
{| 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;">
|<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;">
|}
|}
*Estimated Time <br>
*Estimated Time <br>
20 minutes
*Materials/ Resources needed
*Materials/ Resources needed:
Laptop, Geogebra file, projector and a pointer.
*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any
#Meaning of chord.
# The students should know the basic concepts of a circle and its related terms.
#Meaning of circle.
# They should have prior knowledge of chord and construction of perpendicular bisector to the chord.
*Multimedia resources: Laptop
*Multimedia resources
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets
*Process/ Developmental Questions
*Process:
#what is a chord?
# Show the children the geogebra file.
#The folded line connected from where to where?
# Let them identify the chord. Ask them to define a chord.
#How many chords can be drawn in a circle?
# perpendicular bisector.
# Show them the 2nd chord.
# Let students observe if everytime the perpendicular bisector of the chord passes through the centre of the circle.
*Developmental Questions:
# What is a chord ?
# At how many points on the circumference does the chord touch a circle .
# What is a bisector ?
# What is a perpendicular bisector ?
# In each case the perpendicular bisector passes through which point ?
# Can anyone explain why does the perpendicular bisector always passes through the centre of the circle ?
*Evaluation
*Evaluation
#was the effect of chord in a circle?
# What is the angle formed at the point of intersection of chord and radius ?
#Was the student able to give the meaning of chord?
# Are the students able to understand what a perpendicular bisector is ?
# Are the students realising that perpendicular bisector drawn for any length of chords for any circle always passes through the center of the circle .
*Question Corner
*Question Corner:
#how many chords can be drawn in a circle?
# What do you infer ?
#What happens to the size of the chord if it moves away from the centre?
# How can you reason that the perpendicular bisector for any length of chord always passes through the centre of the circle.
===Activity No # ===
===Activity No # ===
