SEMI-DETAILED LESSON PLAN
School:
Teacher
Date:
I. OBJECTIVES
Central National High School
Alven F. Argel
February 20, 2024
Grade level:
Learning area:
Quarter:
A. Content Standards
9
Mathematics
3rd
The learners demonstrate an understanding of:
1. parallelograms and triangle similarity.
2. Performance Standards The learners should be able to:
investigate analyse, and solve problems involving parallelograms
and triangle similarity through appropriate and accurate
representation.
3. Learning Competencies Learning Competency: Proves the Midline Theorem. (M9GE-IIId-1)
and Objectives
Learning Objectives:
1. State the Midline Theorem
2. Apply the Midline Theorem in solving problems involving
triangles
3. Shows patience and perseverance in applying the Midline
Theorem when solving problems involving triangles
II. CONTENT: THE MIDLINE THEOREM
III. LEARNING RESOURCES
A. References
1. Teachers guide Pages
Pages 216-217
2. Learner’s Material Pages
Pages 327-329
3. Textbook Pages
4. Additional Materials
B. Other Learning Resources
IV. PROCEDURES
Preliminary Activities
1. Greetings
2. Prayer
3. Cleanliness
4. Orderliness (sitting arrangement)
A. Elicit
The teacher ask the student to think of a thing
Reviewing previous lesson or that has a line in the middle or cut in the middle.
presenting the new lesson
Possible answer: folder, globe, roof, basketball
court, badminton court, and etc.
B. Engage
The teacher informs the class to group themselves
with four members each. Ask them to get the
Establishing a purpose for materials that they were asked to prepare: 4 pieces
the lesson
of colored paper, pencil, ruler, adhesive tape, and a
pair of scissors.
Next, the students will be asked to follow the
procedures
given
in
Activity
11:
It’s
Paperellelogram! Found on page 327 of the
learners’ module.
Procedures:
1. Each member of the group shall draw and
cut a different kind of triangle out of the
colored paper ( group 1:equilateral triangle,
2: right triangle, 3: obtuse triangle, and 4:
acute triangle)
2. Choose third side of the triangle. Mark each
midpoint of the other two sides, then
connect the midpoints to form a segment.
Question: Does the segment drawn look parallel to
the third side of the triangle you chose?
3. Measure the segment drawn and the third
side you chose.
Question: Compare the lengths of the segment
drawn and the third side you chose. What did you
observe?
4. Cut the triangle along the segment drawn.
Question: What two figures are formed after
cutting the triangle along the segment drawn?
5. Use an adhesive tape to reconnect the
triangle with the other figure in such a way
that their common vertex was a midpoint
and that congruent segments formed by a
midpoint coincide.
Questions:
1. After reconnecting the cutouts, what new
figure is formed? Why?
2. Make a conjecture to justify the new figure
formed after doing the above activity.
Explain your answer
3. Do you think that kind of findings apply to
all kinds of triangle? Why?
The teacher asked the student to present their
outputs in front
Presenting examples or
instances of the new lesson
Group 1:
Group 2:
Group 3:
Group 4:
4. Explore
The teacher facilitates the students with their
Discussing new concepts findings to lead them to discover the Midline
and practicing new skill #1
Theorem. He/she introduces the Midline theorem
to them after performing Activity 11.
Discussing new concepts Theorem 5: The Midline Theorem
and practicing new skill #2
“The segment that joins the midpoints of two sides
of a triangle is parallel to the third side and half as
long.”
Then, the learners, through the guidance of the
teacher, complete the proof of the Midline theorem
by doing the Show Me! Activity found on page 328
of the Learner’s Module.
Given: HNS , O is the midpoint of HN , E is the
midpoint of NS
Prove:
OE HS
,
OE 
1
HS
2
Answer Key/Proof:
STATEMENTS
REASONS
1. HNS , O is the midpoint of
HN, E is the midpoint of NS
2. In a ray opposite EO, there
is a point T such that OE =
ET.
3. EN  ES
4. 2  3
5. ONE  TSE
1. Given
6. 1  4
6. CPCTC
7. HN ST
7. AIAC, then the lines are
parallel
8. OH  ON
8. Definition of Midpoint
9. ON  TS
9. CPCTC
10. OH  ST
10. Transitive Property
11. Quadrilateral HOTS is a
parallelogram
11.
Definition
parallelogram
12. OE  HS
12. OE is on the side of OT
of parallelogram HOTS
13. OE + ET = OT
13. Segment
Postulate
14. OE + OE = OT
14. Substitution
15. 2OE = OT
15. Addition
2. In a ray, point at a
given distance from the
endpoint of a ray.
3. Definition of midpoint
4. Vertical Angle Theorem
5.
SAS
Congruence
Postulate
of
a
Addition
16. HS  OT
16.
property
17. 2OE = HS
17. Substitution
18.
18. Substitution
OE 
1
HS
2
Parallelogram
(The segment joining the
midpoints of two sides of a
triangle is half as long as the
third side.)
5. Explain
Developing Mastery (Leads
to Formative Assessment)
Let’s Try! (Board work)
The students write their answer on the board base
on the statement and reason given above about
the figure below:
N
W
M
T
R
P
Prove that WT║MP
6. Elaborate
The teacher ask the student about where does the
Finding
practical midline applied in real life situation? (Engineering,
applications of concepts and Carpentry, division of lots and etc.)
skills in daily living
Possible answer: braces of four leg table
Integration of the topic: Araling Panlipunan
(Geography, territory, and etc.), Science (Division
of Cell), Arts (shapes and lines), PE (measurement
of courts; basketball, volleyball, badminton, and
takraw)
Finding
generalizations/ The teacher let the students summarizes the
abstractions
about
the Midline Theorem. The teacher may use the
lesson
following guide questions to elicit learner’s
generalizations:
a.
What is the Midline Theorem all about?
b.
Why it is called midline?
c.
Can you give an example of Midline
theorem in a real-life situation? How can you say
so that it is a midline?
F. Evaluate
The teacher let the students answer the following
exercises individually on their lecture notebooks:
Evaluate Learning
I. In your own words, state the Midline Theorem,
give an example of it and prove at least five
statement and reason.
II.
Given triangle HNS, AB is midline, AB║PI
Apply the Midline theorem in solving problems
involving triangles
1. If PI= 62 cm, find AB
2. If AB= 12.5 cm, find PI
3. If A= x+8 and PI= 5x + 1, find AB and PI
Given HNS , O is the midpoint of HN , E is the
midpoint of NS :
1. If OE = 11, What is the length of HS ?
2. If NH = 42, What is the length of NO ?
3. . If NE = 22, What is the length of ES ?
G. Extend
Additional activities for
application or remediation
4. If HS = 30, What is the length of OE ?
Answer Key:
1. 22
2. 213. 22
4. 15
Assignment:
1. In a short bond paper, create your own real
-life problem that will lead to the application
of the midline theorem. Provide illustration
and label each segment that shows the
midline theorem. Prove using the statement
and reason given on the table above.
Criteria:
Creativity and Originality
Relevance to the topic
Showing correct labels of point/line
Proving
Total
V. REMARKS
VI. REFLECTIONS
A. No. of learners who earned 80% in
the evaluation
B. No. of learners who require
additional activities for remediation
who scored below 80%
C. Did the remedial lessons work? No.
of learners who have caught up with
the lesson
10%
30%
30%
30%
100%
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did this work?
F. What difficulties did I encounter
which my principal or supervisor can
help me solve?
G. What innovation or localized
materials did I use/discover which I
wish to share with other teachers?
Prepared by:
Alven F. Argel
Student-Teacher
Checked by:
Raenalyn M. Supetran
Teacher III
Reviewed by:
STAR L. CABAYAO
Head Teacher II
Noted by:
Jeruel I. Vasquez
Principal IV