Mathematics 8 Lesson Exemplar for Everyday use

Lesson Exemplar

1. 8
Quarter 1
Lesson
7
Lesson Exemplar
for Mathematics
Quarter 2

2. Lesson Exemplar for Mathematics Grade 8
Quarter 2: Lesson 7 (Week 7)
SY 2025-2026
This material is intended exclusively for the use of teachers participating in the pilot implementation of the MATATAG K to 10 Curriculum during the
School Year 2024-2025. It aims to assist in delivering the curriculum content, standards, and lesson competencies. Any unauthorized reproduction,
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Development Team
Writer:
Rener D. Daya (University of Mindanao)
Validator:
Ysmael V. Caballas (Philippine Normal University – South Luzon)
Management Team
Philippine Normal University
Research Institute for Teacher Quality
SiMERR National Research Centre

3. MATHEMATICS / QUARTER 2 / GRADE 8
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A.Content
Standards
The learners should have knowledge and understanding of triangle inequality theorems.
B.Performance
Standards
By the end of the lesson, the learners are able to use the triangle inequality theorems to establish results for angles
and sides in triangles. (MG))
C.Learning
Competencies
and Objectives
Learning Competency
By the end of the lesson, the learners are able to apply the triangle inequality theorems to establish results for angles
and sides in triangles.
Lesson Objectives
1.Correctly illustrate the triangle inequalities of two triangles.
2.Correctly illustrate the hinge theorem.
3.Accurately determine the measures of angles and sides of triangles.
4.Accurately solve problems involving hinge theorem
D.Content Triangle Inequality Theorems (Inequalities in Two Triangles)
Hinge Theorem (SAS Inequality Theorem)
Converse of Hinge Theorem (SSS Inequality Theorem)
E.Integration
II. LEARNING RESOURCES
BYJU'S (2024, May 26). Triangle Inequality Theorem. https://byjus.com/maths/triangle-inequality-theorem/
Hosch, W. L. (2026, May 26). triangle inequality. Encyclopedia Britannica. https://www.britannica.com/science/triangle-inequality
MathBitsNotebook.com (2024, May 27). Hinge Theorem. https://mathbitsnotebook.com/Geometry/SegmentsAnglesTriangles/SATHinge.html
Nivera, G. C., (2018). Patterns and Practicalitities: Mathematics 8. Don Bosco Publishing Antonio Arnaiz Corner Chino Roces Avenues, Makati
City, Philippines.
Pierce, R. Math is Fun. (2022). Triangle Inequlity. https://www.mathsisfun.com/geometry/triangle-inequality-theorem.html
Static (2024, May 27). Inequalities in Two Triangle. https://static.bigideasmath.com/protected/content/pe/hs/sections/geo_pe_06_06.pdf
Study.Com (2024 May 26). Using the Hinge Theorem. https://study.com/skill/learn/using-the-hinge-theorem-explanation.html
Yup (2024, May 27). Hinge Theorem. https://yup.com/math-resources/hinge-theorem/
1

4. III. TEACHING AND LEARNING PROCEDURE NOTES TO TEACHERS
A.Activating Prior
Knowledge
DAY 1
1.Short Review
From the previous lesson, use this activity as a short review to relate the new
lesson.
Complete Me! Complete the table below.
1. You have three strings of lengths 12, 14, and 21 cm. Can these form a
triangle?
Solution:
Sum of Two Sides Comparison Third Side
12+14=26
14+21=35
12+21=33
2.Feedback (Optional)
Based on the activity you had, what do you think our lesson for today?
DAY 1 Time Frame
15 minutes - Review Activity
15 minutes - discussion
15 minutes – lesson activity
10 minutes - feedback and Q&A

Note: Time frames are just
suggestions. It is up to the
teacher if he/she will make it
more flexible. (situation based)
Introduce the lesson by giving
the learner a short review on
the first day. Use one of the
worked examples from the
previous lesson.
After discussion, the teacher
will use the “Complete Me”
activity. Guide the learners in
this activity by giving an
example. This activity may also
be used as a group task in
promoting collaboration
approaches in the class.
After the activity, give short
feedback so that the learners
will know why they are having
that activity. Before proceeding
to the lesson proper, ask some
questions that will link to the
main lesson.
2

5. B.Establishing
Lesson Purpose
1.Lesson Purpose
Essential Questions:
1.How will you prove the Hinge Theorem?
2.How will you prove the Converse of the Hinge Theorem?
3.How can you determine the measure of angles and sides of a triangle?
4.How can solve real-life problems involving the Hinge Theorem?
2.Unlocking Content Vocabulary
Define Me!
Hinge Theorem – If two sides of a triangle are congruent to two sides of
another triangle, and the included angle of the first is larger than the included
angle of the second triangle, then the third side of the first triangle is longer
than the third side of the second triangle.
Teacher’s Key Points
Theorem - A theorem is a proposition or statement that has been
demonstrated to be true through a logical series of arguments and
reasoning, grounded on accepted assumptions and previously proven
theorems.
Converse of a Theorem - A converse is essentially a theorem in reverse
when expressed in an if-then format. It involves switching the IF and
THEN parts of the original statement. Therefore, if the original statement
is IF this, THEN that, the converse would be IF that, THEN this.
For the lesson purpose, you will
introduce the lesson and
discuss its importance using
essential/guide question/s.
Note: Essential questions are
not necessary to be answered in
this part. These questions will
be answered in part of
“learners’ takeaways.”
Guide the learners to unlock
content vocabulary using the
prepared activity.
C.Developing and
Deepening
Understanding
SUB-TOPIC 1: The Hinge Theorem
1.Explicitation
Tell Me Inequally!
Materials: Two Sticks/straws of unequal length, Rubber band.
Directions:
1. Take two sticks or straws of different lengths.
Position them to create an angle. Picture that the
sticks are connected at
point A with a hinge,
and their other ends, B
and C, are joined by a
rubber band.
2. As the hinge is
Give this activity to the learner.
Using the graphic organizer,
before discussing the theorems
let the learners illustrate the
hinge theorem based on the
given “Tell Me in Equally”
activity.
The result of this activity leads
to the Hinge Theorem.
Validate the answer of learners
3

6. opened wider, the rubber band ought to be stretched.
3. What can you say about the length of BC as m∠BAC increase?
DAY 2
Inequalities in Two Triangles
Theorem Hypothesis Conclusion
The Hinge
Theorem
If two sides of a triangle
are congruent to two
sides of another
triangle, and the
included angle of the
first is larger than the
included angle of the
second triangle, then
the third side of the
first triangle is longer
than the third side of
the second triangle.
BC>EF
Converse of
the Hinge
Theorem
If two sides of one
triangle are congruent
to two sides of another
triangle and the third
sides are not
congruent, then the
larger included angle is
across from the longer
third side.
m∠J>m∠M
then continue with the lesson
proper. The teacher may also
add more activities for further
elaboration of the lesson.
Use the worked examples to
give learners a better
understanding of the concept.
DAY 2 Time Frame
5 – minutes review the 2
nd
day
lesson
25 – minutes discussion
35 – minutes lesson activity
giving feedback
4

7. 2.Worked Example
1.In the figure, which side is longer: CA or CD?
Solution:
The figure above shows that ∆ABC∧∆BCD
have congruent sides, AB≅BD and shared a
common side BC.
Since m∠ABC>m∠CBD,by Hinge
Theorem, we conclude that CA>CD.
2.In the figure, which angle is larger: ∠?????????????????? or
∠???????????????????
Solution:
The figure above shows that ∆ABC and
∆BCD have congruent sides AC≅BD and shared
a common side BC.
Since CD > AB, the converse of the Hinge
Theorem, m∠CBD>m∠ACB
3.Application: Dina and Mahal are camping in a mountain park. One
morning, Dina decides to hike to a waterfall. He leaves the camp and goes
5 km east then turns 15
o
south of east and goes two more km. Mahal also
leaves the camp, but instead hikes 5 km west turns 35
o
north of west, and
hikes two more km to the lake for a swim.
a.Draw a diagram to represent a scenario.
b.Who is closer to the camp, Dina or Mahal? Explain.
Answer: Mahal is closer to camp because She only turns 145 degrees
opposite to Dina’s 165 degrees.
5

8. DAY 3
3.Lesson Activity
Let the learner answer the following activities to monitor their level of learning.
1.Use the Hinge Theorem to complete the following pair of sides and angles
using <, >, or =.
2.Dina and Mahal are camping in a mountain park. One morning, Dina
decides to hike to a waterfall. He leaves the camp and goes 6 km east then
turns 30
o
south of east and goes 3 more km. Mahal also leaves the camp
but instead hikes 6 km west turns 10
o
north of west, and hikes 3 more km
to the lake for a swim.
a.Draw a diagram to represent a scenario.
b.b. Who is closer to the camp, Dina or Mahal? Explain
DAY 3 Time Frame
15–minute wrap up (Lesson
Summary and additional
inputs)
20 – minutes QA for learners'
takeaways
20 – minutes writing essay,
feedback.
For sub-topic 2, use the of the
lesson activities form sub-topic
1 that will serve as short review
for this lesson.
After giving the learners a short
activity, relate their answers in
their lesson for Day 2.
Lesson Activity 1 Answer
Key:
1. <
2. =
3. <
4. =
5. <
6. >
Lesson Activity 2 Answer
Key:
Answer: Dina is closer to the
camp.
D.Making 1.Learners’ Takeaways To identify the learners’
6

9. Generalizations 1.How will you prove the Hinge Theorem?
2.How will you prove the Converse of the Hinge Theorem?
3.How can you determine the measure of angles and sides of a triangle?
4.How can solve real-life problems involving the Hinge Theorem?
2.Reflection on Learning
What I know
+
What I’m learning
=
New understanding
takeaways, let them answer
essential questions and make
them provide real-life examples.
It could be a group task or an
individual task.
Use the picture for the
reflection of learners.
IV. EVALUATING LEARNING: FORMATIVE ASSESSMENT AND TEACHER’S REFLECTION NOTES TO TEACHERS
A.Evaluating
Learning
DAY 4
1.Formative Assessment
A.Use the figure below to match the conclusion on the right with the given
information.
AB = BC, m∠1 > m∠2 A. m∠7 > m∠8
AE > EC, AD = CD B. AD > AB
m∠9 < m∠10, BE = ED
C.
m∠3+m∠4=m∠5+m∠6
AB = BC, AD = CD D. AE > EC
B.Use the Hinge Theorem or its converse and properties of triangles to write
DAY 4 Time Frame
30- minutes assessment
25 – minutes checking and
rationalization of answers
Formative Assessment A.
Answer Key:
1. D
2. C
3. B
4. A
Formative Assessment B.
7

10. and solve an inequality to describe a restriction on the value of x.
1. 2.
Solution 1: Solution 2:
C.Problem Solving: Solve the following problems using the concept of Hinge
Theorem.
1.Two groups of bikers leave the same camp heading in opposite
directions. Each group travels 2 miles, then changes direction and
travels 1.2 miles. Group A starts due east and then turns 45° toward
north. Group B starts due west and then turns 30° toward south.
Which group is farther from camp?
Solution:
a. Draw a diagram that represents the situation and mark the given
measures.
Answer:
b. Which group is farther from camp?
Answer:
c. What if? Group C leaves camp and travels 2 miles due north, then
turns 40° toward east and travels 1.2 miles. Compare the distances
from the camp for all three groups.
Answer:
2.Mia and Kurt play with their roller skates at the town oval. From the
Answer Key:
1. x > 7
2. x > 1
Formative Assessment C.
Answer Key:
1. Group A is far from the
camp.
2. Kurt is farther than Mia
from the center of the oval.
8

11. center of the oval, Mia skates 4 meters east and then 5 meters south.
Kurt skates 5 meters west. He then takes a right turn of 70° and skates
4 meters. Who is farther from the center of the oval?
Solution:
a. Draw a diagram that represents the situation and mark the given
measures
Answer:
b. How are 110° and 90° produced?
Answer:
c. What theorem justifies the conclusion that Kyle is farther than
Kerl from the center of the oval?
Answer:
d. Who is farther from the center of the oval?
Answer:
2.Homework (Optional)
1.Writing. Explain why Theorem 6.12 is named the “Hinged Theorem.”
2.Complete the Sentence. In ∆ABC and ∆DEF, AB≅DE,BC≅EF,∧AC<DF.
So, m∠_____ > m∠_____ by the Converse of the Hinge Theorem.
In homework 3–6, complete the statement with < , > , or =.
7. In the diagram, triangles are
9

12. formed by the locations of the
players on the basketball court.
The dashed lines represent the
possible paths of the basketball
as the players pass. How does
m∠ACB compare with m∠ACD?

B.Teacher’s
Remarks
Note observations on any
of the following areas:
Effective Practices Problems Encountered
The teacher may take note of
some observations related to
the effective practices and
problems encountered after
utilizing the different strategies,
materials used, learner
engagement, and other related
stuff.
Teachers may also suggest
ways to improve the different
activities explored/lesson
exemplar.
strategies explored
materials used
learner engagement/
interaction
others
C.Teacher’s
Reflection
Reflection guide or prompt can be on:
principles behind the teaching
What principles and beliefs informed my lesson?
Why did I teach the lesson the way I did?
students
What roles did my students play in my lesson?
What did my students learn? How did they learn?
ways forward
What could I have done differently?
What can I explore in the next lesson?
Teacher’s reflection in every
lesson conducted/facilitated is
essential and necessary to
improve practice. You may also
consider this as an input for
the LAC/Collab sessions.
10