A DETAILED LESSON PLAN IN MATHEMATICS-8

TIME: 1:50-2:40 DATE: March 6, 2025

TEACHER: Deoquino, Ivy C. GRADE&SECTION: Grade 8-Opal

Content Standard

The learner demonstrates understanding of key concepts of inequali es in a triangle, and parallel
and perpendicular lines.

Performance standard

The learner is able to communicate mathema cal thinking with coherence and clarity in
formula ng, inves ga ng, analyzing, and solving real-life problems involving triangle inequali es,
and parallelism and perpendicularity of lines using appropriate an accurate representa ons.

Competency

The learner proves proper es of parallel lines cut by a transversal. (M8GE-IVd-1)

I. OBJECTIVES

At the end of the lesson, the students will be able to…

a. iden fy the different angles formed in a parallel line cut by a transversal,

b. list down congruent angles and supplementary angles, and
c. appreciate the importance of parallelism and perpendicularity in real-life scenario.

II. SUBJECT MATTER

Topic: Proving proper es of parallel lines cut by a transversal

Strategies: Interac ve, Collabora ve, and Discovery Approach

Materials: IM’s, protractor, chalk and chalkboard

Reference: Mathema cs 8 Learners Module, K to 12 Mathema cs Curriculum Guide, Proper es

of Parallel Lines Cut by a Transversal – WOW MATH (youtube.com)

Integra on:

WITHIN CURRICULUM TEACHING AREA:

Derives and applies the slope formula to determine if two lines are parallel or
perpendicular. Code: M8AL-ALh-3

Applies proper es of special pairs of angles (e.g., complementary, supplementary, ver cal
angles) in solving problems. Code: M8ME-IId-2
 ACROSS CURRICULUM TEACHING AREA:

Analyze how geometric concepts, such as angles and alignment, apply to scien fic
principles (e.g. reflec on and refrac on). Code (Grade 8 Science): S8FE-IIIb-28

Draw and interpret architectural and engineering plans using proper geometric tools.
Code (Grade 8 TLE): TLE_IAAD9-12DW-Ia-1

VALUES INTEGRATION: Highlight the role of geometry in na on-building, such as

designing resilient buildings and roads that benefit the community.

III. PROCEDURES

Teacher’s Ac vity Student’s Ac vity

A. Preliminary Ac vi es:
 Opening prayer
 Gree ngs
 Energizer: Simon Says
 Checking a endance
 Recalling classroom rules

B. Developmental Ac vi es
1.Drill: Flash cards
Name or describe the picture:
[possible answer:]

Perpendicular line

Parallel/Parallel line

Angle/Acute angle

Line segment/Segment

Ray
2. Review:
Can you s ll recall our lesson on triangle inequality Yes, ma’am!
theorems? The larger angle is opposite the longer side, and
“Aa→ 𝑆𝑠” what does it mean? the smaller angle is opposite the shorter side.

Great!

A triangle was formed when a transversal cuts two

parallel lines and a perpendicular segment from a
point to a line forms a right angle. How can you prove
that the non-perpendicular line is the longest line? 90o is the largest possible angle formed in the
triangle. Thus, we can say that it’s opposite is
the longest side base on Triangle Inequality
Theorem 2.
Very well said!

3. Unlocking difficul es
Defend it or Deny it: Random students will give a
random number between 1-30. Then, they will pass
the jar with candies for how many mes, depending
on what random number was given. A student who
get the jar will pick a lollipop with a word and may
define, describe, or give an example within 10
seconds. Otherwise, the teacher will help them
understand it.

[the following words may not be picked in an orderly

manner: ]

Adjacent Next to each other

Consecu ve Ex. Consecu ve numbers: 1, 2, 3

Bisector One that divides things into two equal parts

Transversal Line that intersects two or more coplanar lines

C. Mo va on: Story me!

[The teacher will tell a story. The students will listen and
whenever they visualize parallelism and
perpendicularity, they will stand.]

Juliet is a student and VNHS. She is very demure and very

mindful. One day, she went to the library. She looks at
her watch to see how much me is le for her to stay.
The clock shows 9:00 o’clock. Her class will begin at 9:30
so she decided to stay at the library. Looking at the
shelves she no ced that the shelves are arranged in two
columns facing each other. When she was about to get
the book, she saw a guy on the other side of the shelf (students shall stand a er hearing the
with a nameplate. The nameplate tells that he is Romeo. underlined words)
She says, “Hi, Romeo!” Then, there eyes meet.
Pretending to look for other books they both con nue to
walk hoping they’ll meet at the end of the shelf. As they
con nue, however, the shelf and the wall meet with no
gap for the two students to see each other. The end.

Those that you have visualized as parallel and

perpendicular, how will you draw them on the board?

D. ACTIVITY
The class will be divided into two groups, the first
group will work on Figure 1, while the second group
will work on Figure 2.

1 2
3 4
5 6
7 8

Figure 1

Direc ons: Measure the eight angles using your

protractor and list all the inferences or observa on in
the given items.

m∠1=________
m∠2=________ m∠1=135
m∠3=________ m∠2=45
m∠4=________ m∠3=45
m∠5=________ m∠4=135
m∠6=________ m∠5=135
m∠7=________ m∠6=45
m∠8=________ m∠7=45
m∠8=135
Observa ons: ________________________________
m∠6≅ m∠7
m∠6+ m∠5=180O
 100o
2 1
3 4
5 6 80
o

7 8

Figure 2

Direc ons: Find the measure of all the other angles

without using a protractor.
m∠1=________ m∠1= 80O
m∠2= 100O m∠2= 100O
m∠3=________ m∠3= 80O
m∠4=________ m∠4= 100O
m∠5=________ m∠5= 100O
m∠6= 80 O m∠6= 80O
m∠7=________ m∠7= 80O
m∠8=________ m∠8= 100O

How were you able to find all the missing measure of

other angles? m∠1 and m∠2 are linear pair. Thus, the sum of
their measure is 180O. By subtrac ng 100O from
180O and we get the difference 80O for the
m∠1.

E. ANALYSIS
The teacher facilitates the groups on checking other’s
work.

Direc ons: Measure the eight angles using your

protractor and list all the inferences or observa on in
the given items.

m∠1=________ m∠1=135
m∠2=________ m∠2=45
m∠3=________ m∠3=45
m∠4=________ m∠4=135
m∠5=________ m∠5=135
m∠6=________ m∠6=45
m∠7=________ m∠7=45
m∠8=________ m∠8=135

Observa ons: ________________________________ m∠6≅ m∠7/ m∠6+ m∠5=180O

Group 2, please review Group 1’s work and provide

feedback/correc ons. (Group 2 check the calcula ons of group 1)

Now, I want to hear from Group 1.

In Figure 1, what can you say about the angle pairs: ∠1

and ∠2, ∠3 and ∠4, ∠5 and ∠6, and ∠7 and ∠8? They are linear pair.

Why did you say so? because they are both on the same line and has
the sum of 180O
How about the angles: ∠1 and ∠4, ∠3 and ∠2, ∠5 and
∠8? they have the same measure or they are
congruent

Good job!

Now, let’s inspect Figure 2.

100o
2 1
3 4
5 6 80
o

7 8

Figure 2

Direc ons: Find the measures of all the other angles

without using a protractor.
m∠1=________ m∠1= 80O
m∠2= 100O m∠2= 100O
m∠3=________ m∠3= 80O
m∠4=________ m∠4= 100O
m∠5=________ m∠5= 100O
m∠6= 80O m∠6= 80O
m∠7=________ m∠7= 80O
m∠8=________ m∠8= 100O

Now, Group 1, it’s your turn to review the work of Group

2 and provide feedback/correc ons. (Group 1 evaluates the answer of Group 2)
Group2, how were you able to find all the missing
measure of other angles? m∠1 and m∠2 are linear pair. Thus, the sum of
their measure is 180O. By subtrac ng 100O from
180O and we get the difference 80O for the
m∠1.
Well done!

But before we delve into our discussion, let me first

present the learning objec ves for this lesson.

Please read the following:

(Students read in chorus:)
a. iden fy the different angles formed in
a parallel line cut by a transversal,
b. list down congruent angles and
supplementary angles, and
c. appreciate the importance of
parallelism and perpendicularity in
real-life scenario.

Thank you!

F. ABSTRACTION
Parallel lines are coplanar lines that do not intersect.

b
Figure 3

a||b “line a is parallel to line b”

In figure 3, the lines are parallel because they are

coplanar, they do not intersect and they are
equidistant.

Let me show you another illustra on of parallel lines:

Figure 4
↔ ↔
AB || CD “AB is parallel to line CD”
↔ ↔
In figure 4, the arrow symbol on the line suggests that
two lines are parallel.

Figure 5

For Figure 5 the parallel lines are

m||n and o||p.

Figure 6

Here comes the transversal.

Transversal is a line intersec ng two or more coplanar

line at different points.

In Figure 6, line C is the transversal because it

intersects line a and line b.

Try to look at the next figure.

In Figure 7, there is a line that intersects two lines.

However, we cannot consider it as transversal
because the intersec on is only at one point. Thus, we
can say that there is no transversal shown on the
figure.
 Figure 7

Moving on, let’s iden fy the different angles formed by

parallel lines cut by a transversal.

First, let’s label the parts of the parallel lines.

Exterior part

Interior part

Exterior part

Between two parallel lines, we have the interior part.

And the outer part of the parallel lines above and below,
we will call it the exterior part.

Let’s use Figure 1 again.

In the illustra on, we can say that the exterior angles are
∠1, ∠2, ∠7, and ∠8. Then, the interior angles are ∠3,
∠4, ∠5, and ∠6.
Time to delve on the different angles formed on a
parallel line cut by a transversal.

First, we have the corresponding angles. Corresponding

angles are non-adjacent angles. Referring to Figure 1, we
have ∠1 and ∠6, ∠3 and ∠7, ∠4 and ∠8, and ∠2 and ∠5
as our corresponding angles. If you noticed, one of the
angles is an exterior while the other is an interior
since they can’t be next to each other. Also, of we
separate the upper cluster and lower cluster of angles,
we can observe that they are positioned similarly.
Like, ∠2 and ∠5 are both in upper left.

Second, we have the alternate interior angles which are

∠3 and ∠6; and ∠4 and ∠5. While the alternate
exterior angles are ∠2 and ∠8, and ∠1 and ∠7.

Third, we have interior angles of the same side which

are ∠4 and ∠6, and ∠3 and ∠5. And as for the exterior
angle of the same side are ∠2 and ∠7, and ∠1 and ∠8.

As this pair of angles is already known to you, of

course, we will not forget about the linear pair. Linear
pair is a pair of angles on the same line giving a sum
of 180O.

Last but not least, the vertical angles. They are

opposite each other facing the outward directions. So,
our angle pairs in igure one is ∠1 and ∠3, ∠5 and ∠8,
∠2 and ∠4, and ∠6 and ∠7.

Finally, we have named all the different angles formed

in a parallel line cut by a transversal. What we’re
going to do now is compare those pair of angles by
selecting the pair that are supplementary angles or
those that are congruent angles.

135o 45o
45 o
135o
135o 45o
45 o 135o
 80o
80o 100o
100o
80o 100o

If we review the measure of angles on igure 1 and 2

We can justify those two angles with sum of 180O and
those two angles whose angle measure are equal, or I
should say congruent.

Congruent angles would be:

 Corresponding angles,
 Alternate interior angles,
 Alternate exterior angles, and
 Vertical angles

Meanwhile, Supplementary angles:

 Same-side interior angles,
 Same-side exterior angles, and
 linear pairs

Did you understand our lesson on properties of

parallel lines cut by a transversal? Please stand up [expecta on:] (no students stand up to ask for
those who did not understand. clarifica on about the lesson)

If you are still having confusion, may the application

will aid you for your confusions.

G. APPLICATION
Think-Pair-Share:

Figure 8

With your seatmate, write your names on ½ crosswise

paper and create a two-column table. Referring to
Figure 8, list down all the supplementary angles on
 the le column and all congruent angles on the right
column. You have 5 minutes to do that, but I will Supplementary angles Congruent angles
reward the top 3 pairs. Regardless of your correct ∠a and ∠b ∠a and ∠c
answer, the first 3 pairs to finish the ac vity within 4 ∠d and ∠c ∠h and ∠f
minutes will be rewarded. … …

H. Generaliza on
Note that the conclusion to the parallel line is an non-
parallel lines, therefore it is applicable only to parallel
lines. Again, parallel lines are coplanar lines that
never intersect, no ma er how far they extend. And
the transversal that intersects parallel lines forms;
corresponding, alternate and same-side
interior/exterior angles. In real-life applica ons, it can
be re railway tracks, classroom les and so on.

Have you also thought of more real-life applica ons?

IV. EVALUATION

Test I. Examine Figure 9. For each of the indicated angle

pairs, write down the angle pair it is (corresponding,
alternate interior, alternate exterior, same-side exterior
or same-side interior)

h p
k m

e m
j g

Figure 9

Test II. Referring to the same figure on Test I, list at least

two sets of congruent angles and two sets of
supplementary angles based on the proper es of
parallel lines cut by a transversal.

Similar to the ac vity earlier, we will have the top 10 this

me. However, unlike on ½ sheet of paper, you have to
work individually on ¼ sheet of paper. You are given 5
minutes to do that.

V. ASSIGNMENT
 Draw or describe an example of real-life parallel lines cut
by a transversal and trace the parallel lines cut by a
transversal and the angles formed.

Prepared by: Checked by:

IVY C. DEOQUINO ALEXES B. BANDAL

Student Teacher Coopera ng Teacher

Approved by:

LILIA S. MAGISTRADO, EdD

Principal II