Parallelogram - Lesson Plan - Maths - Education - For Student Teachers - (B.Ed Notes)

College: Vijaya Teachers College (CTE)

Batch: 2019 -21

Student Teacher Name: Nagashwini N

SL.No. 1	Subject: Mathematics	Date: 7-9-2021
Name of School: MES, Jayanagar	Unit: Quadrilaterals	Time: 45 min
Standard: 9th std	Topic: Problems based on Properties of Parallelogram

 

 

 

1. Teaching Points

 

1. Properties of Parallelogram

2. Theorem: In a parallelogram, opposite angles are equal

3. Problems: To find the missing angles (Model sum and Drill sum)

 

2. Content Analysis

 

3.

The pupils will

 

	Instructional objective	Task Analysis
1	Explain the properties of Parallelogram	Recall the meaning of parallelogram
		Recall the angle sum property of quadrilateral
		Recognize that the parallelogram has 2 diagonals intersecting each other
		Identify the given 3 examples are associated with parallelogram and all 3 have same properties.
		List the properties of parallelogram
		Explain the properties of Parallelogram
2.	Prove that, In a parallelogram, opposite angles are equal	Recognize that adjacent angles of parallelogram are supplementary using 3 examples with given measurents
		Read the theorem statement
		Identify the geometrical figure to be drawn
		Draw the rough geometrical figure
		Identify what is given
		Write the data in symbolic form
		Identify what should be proved
		Reason deductively that the adjacent angles are supplementary
		Reason deductively that 2 pair of adjacent angles equated
		Reason deductively that by simplifying the equation, opposite angles are equal
		Conclude that opposite angles in parallelogram are equal
		Prove that, In a parallelogram, opposite angles are equal
3	Solve the problems on parallelogram using its properties	Read the problem statement
		Identify the known and unknown parameter
		Recall the transverse line cuts the parallel lines then alternate interior angles are equal
		Recall the angle sum property of traiangle
		Recall that vertically opposite angles are same
		Recall the properties of parallelogram that adjacent angles of parallelogram are supplementary
		Apply the property and calculate the unknown angle
		Solve the problems on parallelogram using its properties

 

 

4. Instructional Strategy

 

1. Properties of Parallelogram

 

Inducto deductive method

 

2. Theorem: In a parallelogram, opposite angles are equal

 

Inducto deductive method

Analytic and synthetic method

 

3. Problems: To find the missing angles (Model sum and Drill sum)

 

Problem solving method

 

5. Instructional Material

 

1. Meaning of parallelogram and its properties

 

3 types of closed figures with 4 sides (congruency triangles of a parallelogram)

 

2. Theorem: In a parallelogram, opposite angles are equal

 

Chart to show the consecutive angles are supplementary (A + D = 180°)

Prove that Opposite angels of parallelogram ABCD are congruent (D = B).

 

3. Problems: To find the missing angles

 

Model sum problem model and chart

 

 

6.

 

Content Analysis	Learning Experience
	Teachers Activity	Pupils Activity
	Good morning teachers
Engaging	Good morning students
	How are you all	Fine mam
	Can you tell me which baranch of mathematics deals with shapes and measurement?	Geometry
	Look at this paper. Show top of the paper, board and tell that this is a plane surface.	yes
	Draw a line with 2 arrows and ask what is this?	line
	Draws another line. Are 2 line meet each other?	no
	What are these 2 line called, which does not meet each other?	Parallel lines
	What are parallel lines?	If 2 lines does not meet each other at both the ends then it is called parallel lines
	Let us look at the two lines AB and CD in figure above. They intersect at point O. What are these lines called?	Intersecting lines
	Draws a closed figure with 4 sides and ask the students, is this a closed or open figure.	Closed figure
	How many interior angle does this closed figure has?	4
	How many sides does this closed figure has?	4
	How many vertices it has	4
	What is this figure called?	quadrilateral
	What is quadrilateral?	It is a closed figure with 4 sides, 4 angles and 4 vertices.
	Do you know any types of quadrilateral?	Square, rectangle
	Parallelogram is a type of quadrilateral with opposite sides are parallel.
	Good
	Once there was a person called Sham who was an architect, living in a village built a wood factory in his friend Kumar’s field. Kumar was told the shape of field is in parallelogram by his friend Sham, but Kumar wanted to find the shape parallelogram field?   Kumar was having 2 measurements given by an an architect Sham.
	Students observe this picture and focus on the measurements.
	Teacher shows a wood factory in the field (Chart), and the shape of field is parallelogram as shown in the figure.
	In Parallelogram ABCD, and O is the center given that angle OAB = 70 degree, OBC = 30 degree and angle AOD = 100 degree. Find all other angles.
	Students do you know how to find all other angles and find shape of parallelogram field?	No response
ICA	In Parallelogram ABCD, and O is the center given that angle OAB = 70 degree, OBC = 30 degree and angle AOD = 100 degree. Find all other angles.
Topic Declaration	Problems based on Properties of parallelogram
Development
1. Properties of Parallelogram	Students observe this is a parallelogram it is divided into 2 triangles.
	What is the sum of interior angles of triangle	180 degree
	How many triangles are there in parallelogram?	2
	Do you know the sum of interior angle of parallelogram equal to?	360 degree
	Now observe this 2 triangles, I superimpose one triangle over other, are they having same shape and same size?	yes
	Are the triangles congruent?	Yes, triangles are congruent
	Teacher demonstartes that 4 triangles formed by diagonals of closed figure are congruent to each other.
	Does in example 1 closed figure, each of the diagonals divides it into two congruent triangles?	Yes, triangles are congruent
	in example 1 If 2 triangles are congruent are sides and angles same or different?	All the sides and angles are same
	Does in example 2 closed figure, each of the diagonals divides it into two congruent triangles?	yes
	in example 2 If 2 triangles are congruent are sides and angles same or different?	All the sides and angles are same
	4 triangles frormed by 2 diagonals of closed figure Are congruent Opposite sides of closed figure are equal Opposite angles of closed figure are equal Opposite sides of closed figure are parallel Example 1 yes yes yes yes Example 2 yes yes yes yes Example 3 yes yes yes yes
	Can you identify the type of closed figure it is?	parallelogram
	What is common in all the 3 examples
	What do you infer from this table	So, in a parallelogram, each of the diagonals divides it into two congruent triangles
		Opposite sides of parallelogram are equal
		Opposite angles of parallelogram are equal
		Opposite sides of parallelogram are parallel
	These are the properties of parallelogram
	Now observe the figure 1, 2 and 3 fro chart
	If a transversal cuts the 2 parallel lines then the sum of corresponding internal angles is 180 degree
	Does transversal cuts 2 parallel lines Identify transversal Identify the adjacent angles Identify the sum of corresponding angles of adjacent sides Figure 1 Parallelogram ABCD Yes, AD||BC AB A, B   A+B = 180 degree   Figure 2 Parallelogram ABCD Yes, AB||CD AD A, D   A+D= 180 degree   Figure 3 Parallelogram ABCD Yes, AD||BC DC   C, D     D+C= 180 degree
	What do you infer from this table?	Adjacent angles of Parallelogram are supplementary
2. Prove that opposite angles are equal in a parallelogram	Given:	Parallelogram ABCD
	To prove:	Angle A = Angle C and Angle B = Angle D
	Proof: Here since the figure is parallelogram ABCD given, Consider AD||BC
	What is angle A+B	180 degree
	Why?	Because adjacent anges of parallelogram are supplementary
	So, Let A+ B = 180 degree be equation 1
	What is angle B+C	180 degree
	Why?	Because adjacent anges of parallelogram are supplementary
	So, Let B+ C = 180 degree be equation 2
	From equation 1 and 2, what we get in LHS and RHS	A+B = B+C
	Simplifying this A+B = B+C what we get ?	A=C
	Here since the figure is parallelogram ABCD given, Consider AB||CD
	What is angle B+C	180 degree
	Why?	Because adjacent anges of parallelogram are supplementary
	So, Let B+ C = 180 degree be equation 1
	What is angle C+D	180 degree
	Why?	Because adjacent anges of parallelogram are supplementary
	So, Let C+ D = 180 degree be equation 2
	From equation 1 and 2, what we get in LHS and RHS	B+C = C+D
	Simplifying this A+B = B+C what we get?	B=D
	Therefore Opposite angles A=C and B=D hence proved
3. Problems on parallelogram based on its properties
Modal Sum	In Parallelogram ABCD, and O is the center given that angle OAD = 80 degree, ODC=23 degree and angle DOC = 117 degree. Find all other angles.	Ans: Angle A = 80+40=120 degree, B = 23+37=60, C = 80+40=120, D = 23+37=60
	Teacher start writing the rough diagram and values on the board.
	How many angles are formed when 2 diagonals intersect each other	4 angles are formed
	What is angle AOB is equal to?	117
	Angle DOC = 117 = AOB, why?	Vertically opposite angles
	What is angle formed at center of a point?	360 degree
	Good
	So what is 117 + 117 is equal to?	234
	What is 360-234 equal to?	126
	What is 126/2 equal to?	63
	So what is angle AOD equal to?	63 degree
	AOD is equal to COB, why?	Vertically opposite angle
	So, what is AOD = COB =63 degree
	Now in triangle AOD, what is angle sum property of triangle say?	The sum of interior angle of triangle is 180 degree.
	So, you know 2 angles, what is the third angle?	180-63+80 = 37 degree
	Consider 2 parallel lines AD and BC, and transvers line AC cutting this parallel lines
	Here, DAO=OCB, why?	Alternate interior angles are same
	So what is DAO=OCB=?	80 degree
	What is OBC =?	37 degree
	What is OBA =?	23 degree
	Apply one property of parallelogram and tell, What is OAB =?	40 degree
	Why?	As adjacent angles of parallelogram is 180 so 180-80+23+37 = 180-140 = 40
	SO now tell me what are the 4 angles of parallelogram formed?
Drill Sum	In a parallelogram ABCD if one angle is A = 50 degree, find all other angles.	Ans: Angle A = 50 degree, B = 130, C = 50, D = 130
Revisit ICA	In Parallelogram ABCD, and O is the center given that angle OAB = 70 degree, OBC = 30 degree and angle AOD = 100 degree. Find all other angles.	Ans: Angle A = 50+70=120 Angle B = 30+30=60, C = 120 D = 60
Application
	If one angle of parallelogram is 90 degree and opposite sides are equal then what is that figure called?	Rectangle
	If one angle of parallelogram is 90 degree and all sides are equal then what is that figure called?	Square
Closure	Students in this class, you have learnt how to solve problems based on parallelogram using its properties. Now I will be ending this class. In next cass you will learn how to prove in parallelogram opposite sides are equal.
Home Assignment	In a paralleleogram ABCD, if Angle DAB = 4c and ADC = 5c, find all other angles	Ans: 5c+4c=180 c= 30 A= 120 degree B= 150 degree C= 120 B = 150