Content Standard: The learner demonstrates understanding of key concepts of parallelograms and
triangle similarity.
Performance Standard: The learner is able to investigate, analyze, and solve problems
involving parallelograms and triangle similarity through appropriate and accurate representation.
Learning Competencies: The learner uses properties to find measure of angles, sides, and other
quantities involving parallelogram (M9GE-IIIb-1).
I. Objectives
At the end of the lesson, the students must have:
a. Identified the different properties of a parallelogram;
b. Used properties to find measure of angles, sides, and other quantities involving
parallelogram; and
c. Explained the value of equality.
II. Subject Matter: Properties of Parallelogram
Reference: Nocon,E. (2011). Math for Engaged Learning: Geometry. Sibs Publishing
House, Inc. pp242-244.
Sources: www.dummies.com/education/math/geometry/propertiesofparallelogram
Materials: power point presentation, visual, printed materials
III. Procedure: 5A’s Method
Teacher’s Activity
Students’ Activity
Preliminaries
Good morning class! Before we start, let us
all stand and have a prayer.
“Let us all remember that we are in the most
holy presence of God… Amen.”
Good morning class!
Good morning sir Keyle!
Before you will take your seats, kindly pickup some pieces of paper on the floor and
arrange your chairs properly at the count of
5. 1, 2, 3, 4, 5.
(Students do as told.)
Alright! You may now take your seats.
Thank you, sir.
How are you today?
We are fine, sir.
It is great that you are all fine because it is an
essential thing to have an enthusiastic and
meaningful learning process today.
Before anything else, I just want to inform
you about my rules that you should follow
for us to have a harmonious relationship in
this class and this rules are abbreviated as
P.R.L.
It stands for Participate, Respect, and Listen.
Are the rules clear class?
Yes, Sir.
Alright! Do we have absentees today?
None, sir.
A. Awareness
1. Review
Let us proceed! What have we discussed last
meeting, class?
Do you have any questions regarding your
previous discussion?
Last meeting we have discussed about
quadrilaterals.
None, sir.
Alright! Let us see if you really have
understood the discussion yesterday. Let us
have an activity. I have prepared a set of
shapes, all you need to do is to identify
whether the shape is a quadrilateral or not.
Say Quad yan if the shape presented is a
quadrilateral, otherwise say Di quad yan. Just
raise your right hand if you want to answer.
Is that clear class?
Yes, sir.
Expected answers:
1. Quad yan!
2. Di Quad yan!
3. Di Quad yan!
4. Quad yan!
5. Quad yan!
Very Good, seems like you did listen to the
discussion yesterday. Please give yourselves a
(Students do as told.)
round of applause for that.
2. Motivation
Class, I have here a picture. I want you to
evaluate properly the picture.
What do you see in the picture?
An eraser, sir.
Now class, take a look at this portion. What
kind of polygon is this portion?
It is a quadrilateral, sir.
That is right! This portion here is a
quadrilateral. Now what type of
quadrilateral is this?
It is a parallelogram, sir.
Very good! This portion here is a
parallelogram. Do you know what makes this
quadrilateral a parallelogram?
No, sir.
Alright!
3. Statement of the Aim
So, this afternoon, we are going to explore the
different properties of parallelogram. I want
you to listen carefully because at the end of
the lesson you are expected to attain the
following objectives. Everyone please read,
begin.
(Students read)
A. Identify the different properties of a
parallelogram.
B. Use properties to find measure of
angles, sides, and other quantities
involving parallelogram.
C. Explain the value of equality.
Are the objectives clear class?
Yes, Sir.
B. Activity
For us to have knowledge on the different
properties of a parallelogram, let us have our
second activity. I will group you into 4 groups.
Each group will be given illustration,
measuring materials, and guide questions.
You are only given 3 minutes to perform the
task. Choose a presenter to present your task
in the class. Is that clear class?
Yes, Sir.
Guide questions
Group 1:
1. What shape is in the figure?
2. What is the measure of each side of
the figure?
3. How can you describe the
measurement of the opposite side?
4. If you extend the opposite sides, do
these sides intersect? If not, what
do you call these lines that do not
intersect?
Group 2:
1. What shape is in the figure?
2. What is the sum of all angles in the
figure?
3. How can you
measurement of
angles?
describe the
the opposite
Group 3
1. What shape is in the figure?
2. How can you describe the
measurement of its consecutive
angles? Or what is the sum of the
consecutive angles?
Group 4
1. What shape is in the figure?
2. How can you describe the two
measurement of each diagonal?
3. What is the figure formed when a
diagonal is drawn?
4. How can you describe the two
triangles?
Is there any question before we start the
activity?
None, sir.
Alright! Your 3 minutes starts now!
(Students do as told)
Time is up! Are you all done?
Yes, sir.
Do you already have representative to present
your answers?
Yes, sir.
Very good! Let us now listen to the
representative of group 1.
C. Analysis
A
D
B
C
Expected answers:
1. Parallelogram
2. The opposite sides are congruent.
3. The opposite sides do not intersect.
Thus, they are parallel
Excellent work group 1. Let us give group 1
three claps, begin!
(Students do as told.)
What is again the shape of the figure formed?
The shape of the figure is a parallelogram, sir.
Exactly! That figure is a parallelogram. How
did the group 1 describe the measurement of
the opposite sides of a parallelogram?
The opposite sides are congruent.
That is right! The opposite sides are
congruent. Now, does the opposite side of the
parallelogram intersects?
No, sir.
Then, what do you call this kind of line that
does not intersect?
The kind of line that does not intersect is a
parallel line, sir.
Very good! Can we consider this side AD and
side AB as a pair of opposite side?
No sir, because opposite side must not be its
consecutive side.
Alright! Instead, this side is a consecutive side
right?
Yes, sir.
Okay! Let us welcome the presenter of group
2.
Expected answer.
A
B
1. The shape of the figure is a
parallelogram.
2. The total measurement of the angles is
D
C
equal to 360 degrees.
3. The opposite angles are congruent.
Great work group 2! Three claps for group 2
begin!
What is again the shape of the figure formed?
That is right! Angle A and angle C is a pair of
opposite angle right? Same as to the
remaining two angles. What did group 2
concluded about this opposite side?
Very good! Let us now proceed to the task
given to group 3.
A
B
110
D
70
70
110
C
(Students do as told.)
The shape of the figure formed is a
parallelogram.
The opposite angles are congruent.
Expected answer.
1. The shape of the figure is a
parallelogram.
2. Consecutive angle measures 180
degrees.
That is right! Let us give group 3 three claps
begin!
Students so as told.
This angle A and this angle D is a pair of
consecutive angles. If this angle is 70 and the
other angle is also 110 degrees what is the
measurement of this consecutive angles?
180 degrees, sir.
That is right! What do you call the angle
wherein the two angles measures exactly 180
degrees?
The angle is called supplementary angles, sir.
Exactly! Let us now proceed to the last group,
the group 4.
A
D
B
C
Expected answers
1. The shape of the figure is a
parallelogram.
2. The two diagonals intersect each
other.
3. A triangle is formed when a diagonal
is drawn.
4. The two triangles are congruent.
Job well done group 4! Let us give them three
claps, begin!
(Students do as told.)
Alright! Group 4 says that the figure is a
parallelogram. Does the diagonal intersect
each other?
Yes, sir.
When we draw a diagonal we can see
another figure which is a triangle. How many
triangles are formed?
There are two triangles formed in each
diagonal, sir.
Correct! And the two triangles are equal.
Right?
Yes, sir.
Very good! You all did great. Let us give
everyone 3 claps, begin!
(Students do as told)
D. Abstraction
Based on the presentation of group 1 what do
you think is our first property?
The opposite sides are congruent and parallel
sir.
Very good! To have a unified property, let us
have this property. Please read!
(Students read.)
Property 1.
Opposite
side
of
a
parallelogram are parallel and
congruent.
For us to better understand our first property,
let us consider this figure.
4cm
L
A
5cm
T
S
Based on the figure what is the measurement
of side LA and side AS?
The measurement of side LA 4cm and side
AS is 5cm.
Exactly! Who can give to the class a pair of
opposite side in this figure?
Side LA and ST is a pair of opposite side
Another pair of opposite side?
Side LT and AS is another pair of opposite
side.
Using the first property, what is then the
measurement of side ST?
The measurement of side ST is 4cm.
Exactly! How about side LT?
The measurement of side LT is 5cm.
Alright! Do you have any questions?
None, sir.
Okay let us proceed! I have here another
figure.
L
3x + 2
E
O
2x + 5]
V
What can you say about the figure?
The figure has 4 sides namely side L, O, V,
and E, sir.
Alright! Who can name to the class one pair of
opposite side in this figure?
One pair of opposite side is side L and V.
Very good! Who can give me another pair of
opposite side?
Another pair is side E and O.
What was again our first property?
The opposite sides of a rectangle are parallel
and congruent.
That is right! That is why we can now say that
L=V and E = O. What is the measurement of
side V and side L?
Side V is (2x + 50)m and side L is (3x + 2)m
Alright! Therefore, 2x + 5 = 3x + 2. We just only
substitute the measurement of each side right?
Who can find the value of x in this expression? Expected answer
2x + 5 = 3x + 2
2x – 3x = -5 + 2
-x = -3
or x = 3
Is the value of x correct class?
Yes, sir.
Now, is this the final measurement of our
side?
No, sir.
What are we going to do next?
We need to substitute x to any expression to
get the measurement of the sides.
That is right! Who can substitute the value of
x and solve for the measurement of the sides? Expected answer
V = 2x + 5
V = 2(3) + 5
V=6+5
V = 11m
That is right! If V is 11m, what is the
measurement of side L?
Side LOis 11m also teacher.
Exactly! And It is based on our first property.
Questions regarding our first property?
None, sir.
Very good!
Now, based on the answers of group 2. What
do you think is our second property?
Very good! To have a unified property, let us
consider this property. Please read, begin!
The opposite angles are congruent and sum
of the angles measures 360 degrees.
(Students read.)
Property 2
The opposite angles of a
parallelogram are congruent.
Alright! Let us consider this figure.
B
E
100
T
80
80
100
S
Who can name to the class a pair of opposite
angles?
Angle B is opposite to angle S.
That is right who can give me another pair of
opposite angles?
Angle E is opposite to angle T.
That is right! Sum of the angles is equal 360
degrees. Right?
Yes teacher.
Is there any questions?
No, sir.
Do you have any questions with regards to
our second property?
None, sir.
Very good!
Based on the answers of group 3. What do
you think is our third property?
Exactly! To have a clear property, let us
consider this. Please read!
Property 3.
The consecutive angles of a
parallelogram are
supplementary.
The consecutive angles of a parallelogram are
supplementary.
(Students read.)
Alright! Let us consider this figure.
A
D
120
60
B
60
120
C
Who can name to the class the consecutive
angles in this figure?
That is right! Who can give me the sum of
each consecutive angle?
Consecutive angles are A and D, A and B, B
and C, and C and D.
180 degrees, sir.
That is right! Sum of each consecutive angle
is equal to 180 degrees.
What do you call the angle wherein the two
angles measures exactly 180 degrees?
The angle is called supplementary angles, sir.
Very good!
Is there any questions?
Alright! Based on the answers of group 4,
What do you think is our fourth property?
Correct! For us to have a clear property, let us
consider this. Please read.
Property 4
The diagonals of a parallelogram
bisect each other where each
diagonal forms two congruent
triangles.
None, sir.
The diagonals of a parallelogram bisects each
other.
(Students do as told.)
For us to better understand this property, let
us consider this example.
K
Y
B
L
E
Who can name to the class one diagonal
present in the figure?
Diagonal KE.
Another?
Diagonal LY, sir.
Alright! These two diagonals meet at one
point which is point B.
What is the measurement of diagonal KN?
Diagonal KN is 7cm, sir
Very good! Based on our property, what is
the measurement of segment KP?
KP is 3.5 cm, sir.
That is right! Are there any questions before
we proceed?
None, sir.
I have here another example.
K
N
S
W
O
Who can give me the diagonals present in
this rectangle?
The diagonals that are present in that
rectangle are diagonal KO and NW.
Alright! These two diagonals meet at point S.
What is the measurement of diagonal KS?
The measurement of diagonal KS is (2) m.
How about the measurement of diagonal
WS?
The measurement of diagonal WS is 4 m.
Based on our fourth property, we can say
that KO = 2m x 2. How did we get the
measurement of the diagonal KO, class?
Exactly! What about the measurement of the
diagonal WN?
Since the diagonals bisect each other, this
means that the measurement of KO is just
twice the measurement of KS.
8m, sir.
Very Good! You already understand the last
property.
Are there any questions?
None, sir.
Very good!
E. Application
For me to check if you understand our
discussion, let us have an activity.
“Spin it to answer it”
I have here problems involving
parallelograms. All your names will be put in
a spinning wheel, the one that will be pointed
by the arrow will be the one to answer the
problem presented in the screen.
Directions: Find the value of x using the
properties of the parallelogram.
Is the directions clear class?
Yes, sir.
Possible Problems:
Expected answer:
4x-10=3x+5
4x-3x=10+5
x = 15
What is the value of X?
What is the value of x?
What is the measure of angle A?
Expected answer:
3x + 120 = 180
3x = 180-120
3x = 60
x = 20
Expected answer:
Angle A is equal to 120
Value Integration
Were we able to solve the different problems
presented class? As well as the activity?
Yes sir.
What can you observe about the opposite
sides, opposite angles, sum of each
consecutive angle of a parallelogram, class?
It is always congruent, sir.
Exactly! What is the meaning of congruent,
class?
Equality, sir.
Now, why is it important to treat every
people equally, class?
Very well said. It is really an achievement to
treat everyone equally. Now, how can you
help promote equality?
It is important to treat every people equally
because it plays a vital role in promoting a
fair and peaceful society, sir.
In school, I will not choose who my friends
will be. Despite the physical appearance,
attitude, or status, I will treat everyone
equally. I will treat everyone as my brothers
and sisters.
That is very good class.
[]\
I.
Evaluation
Directions: On a one whole sheet of paper, use the properties of parallelogram to
find the measure of the sides, angles, and other quantities.
2X
IV.
20
Assignment
Directions: Illustrate the given parallelogram based on the given statements below
and find the measure of its different quantities.
A parallelogram with angle D and U which is a pair of opposite angles, same as
angle S and T. Angle D is adjacent to angle T. The measure of angle D is twice as the
measure of angle S.
Also, a line is formed connecting point S and point T. Line segment DT is (2x + 4)
meters long and line segment SU is (x + 12) meters long.
Find the following:
1. Name the parallelogram.
2. Find the length of segment DT and SU.
3. Find the measurement of angle D, U, S, and T.