Lesson Plan - Cyclic Quadrilaterals - Maths - Education - (B.Ed. Notes)

 

Vijaya Teachers College (CTE)

Jayanagar, Bangalore - 560011

Batch 2019 - 21

Teaching of Pedagogy in Mathematics

Lesson Plan - ICT integrated lesson plan

 

 

Name: Nagashwini N
B.Ed. 2nd sem	Subject: Mathematics	Date:24-8-2020
Class: 9th grade	Unit: Segment of a Circle Topic: Cyclic Quadrilateral	Time: 40 min

 

Teaching point:

1. Cyclic Quadrilateral

 

Content Analysis:

 

• In a cyclic quadrilateral (Concept), the sum of each pair of opposite angles is 180 degrees. If a quadrilateral has one pair of opposite angles that add to 180, then you know it is cyclic.

   

• A trapezoid is cyclic if, and only if, it is isosceles. (Fact)

   

• To prove that the sum of each pair of opposite angles is 180 degrees. (Procedure)

   

Instructional Objectives:   Knowledge: Students will be able to 1. Recall the definition of quadrilaterals 2. List the properties of quadrilaterals 3. Recall that angles in same segment of circle are equal.   Understanding: Students will be able to 1. Identify that angles in same segment of circle are equal. 2. Identify the cyclic quadrilaterals   Application: Students will be able to 1. Solve the problems related to segment of a circle

Previous Knowledge Assumed: Quadrilaterals, Circle, Segment of a circle

Teaching Materials/Aids: Blackboard, Chalk, Duster, Charts, TLM based on the content, Geogebra files, Images, Video and Audio files, Animation using presentation.

Teaching Methods: Inducto – Deductive method.

Activities: Learning together team

Reference: J.V. Narlikar and memebers, 2006, Mathematics Textbook for Class 9, NCERT, New Delhi.

 

Engaging:

 

T: Good morning students

S: Be attentive in the class, be ready with your pen and book, when I say you to do the calculations, do in your book and tell me the answer.

 

T: In today's class we will learn about cyclic quadrilateral.

T: Cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.

 

 

 

 

 

 

Approach: Inductive method

 

Example 1: (Only Induction method)

 

Activities: Learning together team

A child measures each and every inscribed quadrilateral ( a four sided figure whose vertices all lie on a circle ) and concludes that, “Sum of pair of opposite angles of every cyclic quadrilateral is equal to 180 degrees”

 

 

 

 

 

 

 

lization

 

Teacher activity	Student Activity
Look at the figure example 1 and tell me what are the angles of quadrilateral?	Angle a = 100, angle b = 40, angle c = 80, angle d = 140.

 

What are the pair of opposite angles in this quadrilateral?	Angle a and angle c and angle b and angle d
what is the sum of opposite angle a + angle c in this quadrilateral?	100+80 = 180
what is the sum of opposite angle b + angle d in this quadrilateral?	40+140 = 180
Look at the figure example 2 and tell me what are the angles of quadrilateral?	Angle a = 90, angle b = 90, angle c = 90, angle d = 90.
What are the pair of opposite angles in this quadrilateral?	Angle a and angle c and angle b and angle d
what is the sum of opposite angle a + angle c in this quadrilateral?	90+90 = 180
what is the sum of opposite angle b + angle d in this quadrilateral?	90+90 = 180
Now tell me by looking at the 2 examples what are the sum of opposite angles?	Its is 180 degree
Teacher will analyze and conclude that the sum of the opposite angles of cyclic quadrilateral is 180 degree	Student will conclude that The sum of either pair of opposite angles is cyclic quadrilateral is 180 degree. (Generalization)

Deductive method: Generalization to examples

 

Teacher activity	Student Activity
Teacher will tell that The sum of either pair of opposite angles is

 

cyclic quadrilateral is 180 degree. (Generalization)
And ask students to find the missing angle in the cyclic quadrilateral.
Look at the figure example 1 and tell me what you need to find out?	Missing angle of cyclic quadrilateral
What are the given angles of quadrilateral?	Angle a = 100, angle b = 40, angle c = 80, angle d = x.
What are the pair of opposite angles in this quadrilateral?	Angle a and angle c and angle b and angle d
what is the sum of opposite angle a + angle c in this quadrilateral?	100+80 = 180
what is the sum of opposite angle b + angle d in this quadrilateral?	40+x = 180
What is value of x	X = 140

Approach: Inducto - deductive method

 

 

T: Given a cyclic quadrilateral CBDE.

T: You can observe that there are 4 segments c1, b1, d1, e1.

 

T: In previous class, we have learnt the theorem, that the angles in same segment of circle are equal.

 

T: In the figure you can see that there are two angles present in each segment

 

T: Now observe the figure and tell me, In segment c1, what is angle CED is equal to ?

P: Angle CED is equal to CBD

T: Similarlly observe the figure and tell me, In segment e1, what is angle EBC is equal to ?

P: Angle EBC is equal to CDE

T: Similarlly observe the figure and tell me, In segment d1, what is angle DCB is equal to ?

P: Angle DCB is equal to DEB

T: Similarlly observe the figure and tell me, In segment b1, what is angle BDE is equal to ?

P: Angle BDE is equal to BCE

T: Now in quadrilateral, observe that angle CEB is the sum of angle CBD and DEB.

T: Now tell me, what is the sum of angle CDE and EDB equals?

S: Angle BDC

 

T: Now tell me, what is the sum of angle CBD and CBE equals?

S: Angle EBD

 

T: Now tell me, what is the sum of angle DCB and BCE equals?

S: Angle DCE

 

 

T: Now given the angles of all the segments of a circle, we need to find the angles of quadrilateral.

 

 

 

Angle	Angle	Angle	Angle	Angle	Angle	Angle	Angle	CEB +	EBD +
CED	EBC	BDE	DCB	CEB =	EBD =	BDC =	DCE =	BDC	DCE
equal to	equal to	equal to	equal to	CBD +	CBD +	CDE +	BCE +
CBD	CDE	BCE	DEB	DEB	CDE	BCE	DEB
20	80	60	20	20 + 20	20 + 80	60 + 80	20 + 60	180	180
				= 40	= 100	= 140	= 80
50	70	20	40	50 + 40	50 + 70	70 + 20	20 + 40	180	180
				= 90	= 120	= 90	= 60
20	90	30	40	20 + 40	20 + 90	90 + 30	30 +40	180	180
				= 60	= 110	= 120	= 70

 

Example 1:

T: From table observe the angles of segment and tell me what is angle CEB of quadrilateral?

S: 20 + 20 = 40

T: From table observe the angles of segment and tell me what is angle EBD of quadrilateral?

S: 20 + 80 = 100

T: From table observe the angles of segment and tell me what is angle BDC of quadrilateral?

S: 60 + 80 = 140

T: From table observe the angles of segment and tell me what is angle DCE of quadrilateral?

S: 20 + 60 = 80

 

T: What is angle E + angle D are they adjacent or opposite angles?

S: Opposite

T: What is angle E + angle D are they adjacent or opposite angles?

S: 180

T: What is angle B + angle C are they adjacent or opposite angles?

S: Opposite

T: What is angle B + angle C ?

S: 180

 

 

Example 2:

 

T: From table observe the angles of segment and tell me what is angle CEB of quadrilateral? S: 50 + 40 =

S: 90

T: From table observe the angles of segment and tell me what is angle EBD of quadrilateral? S: 50 + 70 =

S: 120

T: From table observe the angles of segment and tell me what is angle BDC of quadrilateral? S: 70 + 20 =

S: 90

T: From table observe the angles of segment and tell me what is angle DCE of quadrilateral? S: 20 + 40 =

S: 60

 

T: What is angle E + angle D are they adjacent or opposite angles? S: Opposite

T: What is angle E + angle D are they adjacent or opposite angles? S: 180

T: What is angle B + angle C are they adjacent or opposite angles? S: Opposite

T: What is angle B + angle C ?

S: 180
S: 180

 

Example 3:

 

T: From table observe the angles of segment and tell me what is angle CEB of quadrilateral? S: 20 + 40 =

S: 60

T: From table observe the angles of segment and tell me what is angle EBD of quadrilateral? S: 20 + 90 =

S: 110

T: From table observe the angles of segment and tell me what is angle BDC of quadrilateral? S: 90 + 30 =

S: 120

T: From table observe the angles of segment and tell me what is angle DCE of quadrilateral? S: 30 +40 =

S: 70

 

T: What is angle E + angle D are they adjacent or opposite angles? S: Opposite

T: What is angle E + angle D are they adjacent or opposite angles? S: 180

T: What is angle B + angle C are they adjacent or opposite angles? S: Opposite

T: What is angle B + angle C ?

 T: What do you observe from the last 2 columns of the table? S: All the angles are 180 degree

T: Are angle E + angle D is same in all the examples of cyclic quadrilateral? S: Yes

T: Are angle B + angle C is same in all the examples of cyclic quadrilateral? S: Yes

 

T: Can you tell me what do you infer from this table?

S: Angle E + angle D and angle B + angle C is always 180 degree in cyclic quadrilateral.

Generalization:

T: Thus, the sum of either pair of opposite angles of cyclic quadrilateral is 180 degree.

 

T: Now let us apply this rule to solve the problems using the cyclic quadrilateral theorem.

 

T: In previous examples you knew all the angles of a segment. But now you need to find the angle of a segment, by using the property of cyclic quadrilateral. 

 

 

 

 

 

 

 

Angle	Angle	Angle	Angle	Angle	Angle	Angle	Angle	CEB +	EBD +
CED	EBC	BDE	DCB	CEB =	EBD =	BDC =	DCE =	BDC	DCE
equal to	equal to	equal to	equal to	CBD +	CBD +	CDE +	BCE +
CBD	CDE	BCE	DEB	DEB	CDE	BCE	DEB
60	60	(?)	30	60+ 30	60 +  60	60 +  (?)	30 +  (?)	180	180
				= 90	= 120	= 90	= 60
60	60	30	30	60+ 30	60 +  60	60 +  30	30 +  30	180	180
				= 90	= 120	= 90	= 60

 

Non Example

 

20	90	40 (X)	40	20 +  40	20 +  90	90 +  40	40 +40	190 (X)	190  (X)
				= 60	= 110	= 130	= 80  (X)
						(X)

 

My Reflections/ Experience of using the ICT tool Geogebra:

 

I had wonderful experience of using this ICT tool called Geogebra. It was very easy for me to use this tool to create examples of cyclic quadrilateral with dynamic measurements, which is very difficult to do with out this tool. When I had to present this lesson plan, I was worried regarding the presentation, thanks to geogebra that made this skill of illustration approach very easy. I was able to deliver this lesson plan successfully in front of my the observer and teacher. Creating 4 angles of cyclic quadrilateral which is inscribed on a circle is a complicated task, if tried to attempt it manually by construction method. But this geogebra tool made this complex task easy like a magic and also I was able to do this in short period of time.

Also doing just one working file, I was able to create plenty of images with different measurements.

I was able to extract this file as png format and use it in my lesson plan. I was able to create screen recording of the presentation as mp4 format, so that without any software installation on others computer can, we can use this video to show the demo or presentation, so it is supported on any operating system, it also works offline.

I also like to thank the IT for change team for letting me know about this Geogebra tool, which was useful for me while presenting my skill at VTC. While preparing and presenting my skill, the use of this tool made me confident to move forward to use illustration method prove this theorem with Inducto deductive approach. I am sure that in real classroom students will better understand this concept if I use the images from geogebra. In my career I will surely use this tool effectively to transact the lessons to students without fail. I am glad that this type of free software are helping the teachers in plenty of ways across the globe.