I.
OBJECTIVES
1. Define and illustrate parallel
and transversal line
2. Define and illustrate the pairs
of angles formed by parallel lines cut by a transversal
3. Determine the relationship
between pairs of angles formed by parallel lines cut by a transversal
4. Show cooperation and
participation in doing task and in class discussion
5. Relate the topic in real life
situation and in GAD
II.
SUBJECT MATTER
a. TOPIC: Parallel lines cut by a
transversal
b. SUBTOPIC: Angles Formed by
Transversal
c. REFERENCE: Math Made Easy For
Grade 8 by Beverly A. Domingo, Basilisa Victorina P. Mandac,
and Neva A. Manding, Pages 130-132
Geometry Textbook for
Third Year by Soledad Jose-Dilao and Julieta G.Berbabe,
Pages 421-425
Online Reference:
d. MATERIALS: Visual aids, instructional
materials, video presentation, chalk, blackboard, and eraser
III.
PROCEDURE
TEACHER’S
ACTIVITY
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STUDENT’S ACTIVITY
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A. PRELIMINARY ACTIVITY
Prayer
Greetings
Classroom Management
Checking of Attendance
B. MOTIVATION:
VIDEO PRESENTATION
I have
here a video presentation class which may help you get an idea what are going
to discuss. Please watch carefully and take down notes.
(Playing
Video Presentation)
From
the video that you have watched, what is dominant mathematical figure did you
saw class? Yes, Kish.
Yes,
that’s right. What can you say about the parallel lines in the video? Yes,
Summer.
Definitely
class! So, can you give me the use of parallel lines from the video that you
have watched?
Very
good! What else? Yes, Ace.
That’s
right class! Parallel lines are very important in our life. We see them and
at the same time we use them.
C.
PRESENTATION OF THE TOPIC
So,
today we are going to discuss the pairs of angles when parallel line cut by a
transversal.
D.
LESSON PROPER
Let’s
have first unlock or give the meaning of the word parallel line and
transversal by using pictures.
I have
here pictures where we can see parallel lines.
        
Through these pictures class, do you have an idea what
parallel lines are? Yes, Irene.
Yes, that’s right! Parallel lines are coplanar lines that
do not intersect. || symbol for parallelism means “parallel to”. When we say
coplanar lines, these are lines that lie on the same plane.
I have pictures that illustrate transversal line class.
     
So,
what can you say about transversal line class? Yes, Lewis.
Very
good idea!
Transversal is a line that intersects two or more coplanar
lines at different points.
If two parallel lines cut by a transversal, then there
exist some relationships between pairs of angles formed.
We have 8 angles form when two parallel lines cut by a
transversal.
∠ 1, ∠ 2, ∠ 3, ∠ 4, ∠ 5, ∠ 6, ∠ 7, and ∠ 8.
There are 3 types of angles that are congruent and 2 types
of supplementary angles that are
formed.
3 Types Of Angles that are Congruent
1. Corresponding Angles - are two nonadjacent angles, one
interior and exterior on the same side of the transversal.
Let’s unlock first the unfamiliar words.
What are the words that unfamiliar to you class? Yes,
Camila.
Nonadjacent means not close or near.
Interior means? Yes, Margarette.
That’s right! How about exterior? Yes, Cristel.
Very good! Now, we can easily identify the corresponding
angles.
Let me name one class.
∠ 1 and ∠ 5 and ∠ 1 ≅ ∠ 5.
What else are the corresponding angles? Yes, Aldrin.
Another? Yes, Summer.
And last? Yes, Wrency.
Very good! Did you understand class?
2. Alternate Interior Angles
What do you mean by alternate class? Yes, Ashley.
That’s right!
So,
when we say Alternate Interior Angles are two nonadjacent interior angles on
opposite sides of the transversal.
We
have two pairs of Alternate Interior Angles.
We
have ∠
4 and ∠
6, ∠
4 ≅ ∠ 6.
What
is the other? Yes, Julia.
Very
good! Did you get it?
If
we have alternate interior angles, we also have alternate exterior angles.
3.
Alternate Exterior Angles – are two nonadjacent exterior angles on opposite
sides of the transversal.
We
have two pairs of Alternate Exterior Angles.
Can
you name one? Yes, Serwyn.
The
other one. Yes, Sandara.
Very
good! Can you follow class?
Next is the 2 types of
supplementary angles.
By the way, what do you mean by supplementary angles class?
Yes, Gizelle.
Excellent!
Supplementary angles are two angles that when you sum up it is equal to 1800.
4. Same Side Interior Angles – two nonadjacent interior
angles that lie on the same side of the transversal
There are two pairs of angles. Can you name one? Yes,
lewis.
Another? Yes, Gian.
Very good! Can you follow class?
5. Same Side Exterior Angles - two nonadjacent exterior
angles that lie on the same side of the transversal.
There are two pairs also. Can you name one? Yes, Gerald.
The other one. Yes, Una.
Very good! Did you all understand class?
If you really understand our lesson class. Let have an
acivity.
E. FIXING SKILLS
ACTIVITY: STEP ON ME: AM I YOUR TYPE OF ANGLE?
The class will be divided into 6 groups. Each group must have
5 representatives.
Here is the mechanics.
Each group has a parallel line cut by a transversal on the
floor set by the teacher.
The teacher will dictate a type of angles for example
corresponding angles, then each first member of each group will step on the
pair of corresponding angles on the floor. The first member who will step the
type of angle that the teacher dictated will have the point.
The group which have the highest points will be the winner
and received a prize later on.
(Video presentation for the activity)
Are you ready?
Announcing the winning group.
Arrange your chairs class.
Let’s have a summary on what we had discussed class.
IV. GENERALIZATION
Inside this box are the meaning of the words that was
posted on the board class.
V. VALUES INTEGRATION
In the society class, boys and girls are everywhere. Am I
right?
Can you give me an example where you can find boys and
girls?
That’s right! Isn’t that boys and girls have there right
and roles?
Can you give me an example of there rights and roles? Yes,
Georgyna.
Yes, that’s true. What about their roles? Yes, Princess.
That’s right! What else?
Very good class!
Another thing is, boys
and girls must respect women as well as men.
Nowadays,
we are lack of respect to other people which is often lead to fights and
misunderstanding.
Relating
it to our topic, girls and boys are like parallel lines cut by a transversal.
Boys and girls are the parallel lines and that transversal is God. When God
cut the misunderstanding and fights within us, that’s when he give his equal
love and understanding despite of our flaws in life. I just want to leave a
quote,
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Lines
Ma’am, specifically parallel lines.
Parallel
lines are used every day and we can see them everywhere like at the train
station, parking lot, forest, and high ways and even inside of our house
Ma’am.
From
the video, parallel lines are used as a design in establishing structure like
temple and public buildings Ma’am.
Parallel
lines are used in making railroad track, power line, fences, stairs, and even
strings of guitar.
Parallel
lines are coplanar lines that do not intersect.
It is a line that intersect at parallel lines Ma’am.
Nonadjacent, Interior, and
Exterior Ma’am.
Inside
Ma’am.
Outside
Ma’am.
∠ 4 and ∠ 8, ∠ 4 ≅ ∠ 8.
∠ 2 and ∠ 6, ∠ 2 ≅ ∠ 6.
∠ 3 and ∠ 7, ∠ 3 ≅ ∠ 7.
Yes,
Ma’am,
Opposite
Ma’am.
∠
3 and ∠
5, ∠
3 ≅ ∠ 5 Ma’am.
Yes,
Ma’am.
∠
1 and ∠
7, ∠
1 ≅ ∠ 7.
∠
2 and ∠
8, ∠
2 ≅ ∠ 8.
Yes,
Ma’am.
Two
angles that when you sum up it is equal to 1800 Ma’am.
∠
3 and ∠
6, m∠3
+ m∠6
= 180.
∠
4 and ∠
5, m∠4
+ m∠5
= 180.
Yes,
Ma’am.
∠1
and ∠
8, m∠1+
m∠8
= 180.
∠2
and ∠
7, m∠2+
m∠7
= 180.
Yes,
Ma’am.
Yes,
Ma’am.
Parallel
lines are coplanar lines that do not intersect.
Transversal is a line that intersects two or more coplanar
lines at different points.
Corresponding Angles are two nonadjacent angles, one
interior and exterior on the same side of the transversal.
Alternate
Interior Angles are two nonadjacent interior angles on opposite sides of the
transversal.
Alternate
Exterior Angles are two nonadjacent exterior angles on opposite sides of the
transversal.
Same Side Exterior Angles two nonadjacent exterior angles
that lie on the same side of the transversal.
Same Side Interior Angles two nonadjacent interior angles
that lie on the same side of the transversal.
Supplementary angles are two angles that when you sum up it is equal to 1800.
Yes,
Ma’am.
In the
school, at the park, in the office, public places and many more Ma’am.
Yes,
Ma’am.
Boys
and girls have the right to study, right to be love, right to be respected
and many more.
Boys
and girls must be a role model to everyone.
Boys
and girls must protect women as well as men. Girls and boys must aware of
his/her own action and words so that she/he cannot hurt or damage people.
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VI. EVALUATION
In the figure, l || m and p || q. Determine the relationship
that exist between each pair of angles below and tell if they are congruent or
supplementary.
ANGLE PAIRS
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RELATIONSHIP
(Corresponding
Angles (CA), Alternate Interior Angles (AIA), Alternate Exterior Angles
(AEA), Same Side Interior Angles (SSIA), Same Side Exterior Angles (SSEA) )
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CONGRUENT OR
SUPPLEMENTARY
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1.
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∠ 1 and ∠ 7
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Alternate Exterior Angles (AEA)
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CONGRUENT
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2.
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∠ 4 and ∠ 8
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Corresponding Angles (CA)
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CONGRUENT
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3.
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∠ 3 and ∠ 6
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Same Side Interior Angles (SSIA)
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SUPPLEMENTARY
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4.
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∠ 5 and ∠ 3
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Alternate Interior Angles (AIA)
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CONGRUENT
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5.
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∠ 8 and ∠ 11
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Same Side Exterior Angles (SSEA)
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SUPPLEMENTARY
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6.
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∠ 2 and ∠ 13
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Same Side Interior Angles (SSIA)
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SUPPLEMENTARY
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7.
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∠ 9 and ∠ 15
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Alternate Interior Angles (AIA)
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CONGRUENT
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8.
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∠ 11 and ∠ 14
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Same Side Exterior Angles (SSEA)
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SUPPLEMENTARY
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9.
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∠ 12 and ∠ 13
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Same Side Exterior Angles (SSEA)
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SUPPLEMENTARY
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10.
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∠ 9 and ∠ 16
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Same Side Interior Angles (SSIA)
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SUPPLEMENTARY
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VII. ASSIGNMENT
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Given the figure at the right, fine the value of x that makes m || n. Also,
find the angle measure of the given pair of angles using the solved value of x.
1. m∠2= 4x-2 ; m∠3=2x-4
x =______, m∠2 =______, m ∠3 = _________.
2. m ∠2=3x+1; m ∠4= 5x-7
x =______, m∠2 =______, m ∠3 = _________.
Reference: Math
Made Easy For Grade 8 by Beverly A. Domingo, Basilisa Victorina P. Mandac, and Neva A. Manding, Page 132
