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DAILY
LESSON
PLAN
School
Dumaguete City High School
Year Level
GRADE 9
Teacher
Livingstone M. Abasola; Craig N.
Refugio, PhD
Descriptive title
Mathematics
Teaching Dates
February 11 ,2019
Quarter
Fourth
DAY OF THE WEEK
Monday
SECTION & TIME
Platinum 9 (7:30-8:30am) and Oxygen 9 (10:50-11:50 am)
I. OBJECTIVES
A. Content Standards
The learners demonstrate understanding of key concept of
parallelograms and triangle similarity.
B. Performance Standards
The learner is able to investigate, analyze, and solve problems
involving parallelogram and triangle similarity through appropriate
and accurate representation.
C. Learning Competencies/
Objectives
(Write the LC Code for
each)
Proves the Pythagorean theorem. M9GE- IIIi-2
At the end of one hour period (60 minute), the students will be able
to:
Knowledge
state the Pythagorean Theorem.
Skills
prove the Pythagorean Theorem.
Attitudes
develop patience and perseverance in solving problems
using Pythagorean Theorem.
II. CONTENT
“The Pythagorean Theorem and Its Proof”
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages
Teachers Guide in Mathematics 9: Pages 356 - 357
2. Learner’s Materials
pages
Mathematics 9: Learner’s Materials (389-392)
3. Textbook pages
ꬲ - Math 9 by Orlando A. Oronce and Marilyn O. Mendoza
(pages 348 - 352)
4. Additional Materials
from Learning Resource
( LR) Portal
https://www.depednegor.net
patreon.com/Teded
https://www.ixl.com
B. Other Learning
Resources
Visual aids, Speaker and Activity Sheets
IV. PROCEDURES
A. Reviewing previous
lesson or presenting the
new lesson
What was our topic last meeting?
Triangle Proportionality Theorem
Can you State Triangle Proportionality Theorem?
Triangle proportionality Theorem
If a line parallel to one side of a triangle intersects the
other two sides, then it divides those sides proportionally.
B. Establishing a purpose
for the lesson
Present the objectives to be achieved at the end of the lesson:
state the Pythagorean Theorem.
prove the Pythagorean Theorem.
develop patience and perseverance in solving problems using
Pythagorean Theorem.
C. Presenting examples/
instances of the new
lesson
(Story Telling)
There was a boy name David. David and his family was living
besides a big tree and a river. His father was a carpenter, and that
makes David also wanted to become an Engineer. He shows more
interest about mathematics, he always apply mathematics on the
things that he usually uses.
One day, while David was playing his kite on the other side of the
river, it was accidentally stuck at the top of the tree. Luckily he was
able to measure the length of the thread he uses before playing
which measures 20 meters.
Then, since, he has been crossing the bridge for a long time, he
already knew the length of the bridge which is 12 meters.
Until one day, when he was about to cross the bridge going to
school, he noticed that the bridge was already destroyed. He
doesn’t want to be absent on that day because they will have an
exam. And suddenly a great idea came to his mind. He needs to cut
the tree to replace the bridge. But he was not sure that the length of
the tree is longer or equal to the length of the bridge. How could
David make sure that if he cut the tree it would reach to the other
side of the bridge?
(He is going to find the length of the tree)
D. Discussing the new
concepts and practicing
new skills #1
(Discuss the Pythagorean Theorem)
Pythagorean Theorem
(Recall the name of the sides of a right triangle)
Hypotenuse
The longest side of a right triangle, opposite to the right angle.
The other two sides of a right triangle is called legs.
Given
LM = r and MN = S as
the legs
LN = t as the hypotenuse
<LMN is a right angle
Prove:
222 srt
Proof:
Construct altitude MK =
w to the hypotenuse LN
= t, dividing it to LK = u
and KN = c
1. Discussing the new
concepts and practicing
new skills #2
(Discuss the proof of Pythagorean Theorem)
HINTS
STATEMENTS
REASONS
1.Describe triangles
LMN, MKN and LKM
when an altitude MK
is drawn to its
hypotenuse.
Right Triangle
similarity Theorem
2. Write the
proportion involving
Special Property of
Equality
M
N
t
L
s
r
r
L
K
M
t
N
s
s
w
u
r
v
the geometric
means r and s
3.Cross multiply the
terms of the
proportions in
statement 2.
Cross- Multiplication
Property of
Proportion
4.Add
2
s
to the both
sides of
utr
2
in
statement 3
Addition property of
Equality
5.Substitute
2
s
on
the right side of
statement 4 suing its
equivalent from
statement 3.
Substitution
6.Factor the right
side of statement 5.
Common Monomial
Factoring
7.Substitute u + v in
statement 6 by its
equivalent length in
the figure.
Segment Addition
Property
8.Simplify the right
side of statement 7.
Product Law of
Exponents
1. Finding practical
applications of concepts
and skills in daily living
(Solve the height of the tree)
Let:
c be length of the thread
b length of the bridge
a height of the tree
Formula:
222 bac
a
a
a
a
a
a
16
256
256
144400
1220
1220
2
2
2
222
222
Therefore, the height of the tree is 16 meters.
Bridge (12
meters)
Length of the
Thread (20
meters)
Tree
3. Developing
mastery(Leads to
formative assessment)
(Group the students into three groups. The bases of the groupings
would be the colors of trips of papers during their attendance )
Group 1:
Bella is admiring a statue in Lowell park from 16 feet away. If
the distance between the top of the statue to Bella’s head is 20 feet,
how much taller is the statue?
Group 2:
A bird was sitting in 8 feet away from a mango tree and flew
17 feet to reach at the top of the tree. How tall is the tree?
Group 3:
The foot of a ladder is placed 6 feet from a wall. If the top of the
ladder rests 8 feet up on the wall, how long is the ladder?
4. Finding practical
applications of concepts
and skills in daily living
How would you able to apply your knowledge about Pythagorean
Theorem in real world?
5. Making generalizations
and abstractions about
the lesson
What is formula of Pythagorean Theorem?
222 bac
Who can state the Pythagorean Theorem?
Pythagorean Theorem
The square of the hypotenuse in a right triangle is equal to the
sum of the squares of the legs.
6. Evaluating learning
(1/2 Crosswise) Solve for the unknown side.
1.
2.
3.
7. Additional activities for
application or
remediation
Read and study in advance about “Is the Triangle Right, Acute or
Obtuse?” on pages 392 - 393
V. REMARKS
VI. REFLECTION
3
4
?
17
8
?
?
6
10