Detailed Lesson Plan
School:
Teacher:
Date & Time
Nabua National High School
FRANCIA P. FLORECE
FEBRUARY 27, 2020
Grade Level:
Learning Area:
Quarter:
9
Mathematics
FOURTH
I. OBJECTIVES
A. Content Standard:
The learner demonstrates understanding of the key
concepts of parallelograms and triangle similarity.
B. Performance Standard
The learner is able to investigate, analyze, and solve
problems involving parallelograms ad triangle similarity
through appropriate and accurate representation.
C. Learning Competencies/Objectives
Students are expected to:
a. prove the Right Triangle similarity theorem; (M9GEIIIg-h-1)
b. determine similar right triangles inscribed in a larger
triangle;
c. find the length of an altitude and leg of right triangle
using geometric mean
II. CONTENT
III. LEARNING RESOURCES

Topic: Similarity in Right Triangles
Teaching Strategies: Cooperative learning, ICT
integration
Values Integration: Cooperation, Speed and Accuracy
Speaker, octahedron,bottle with questions, tarpapel,
cartolina, triangles,calculator, projector, laptop, bell, ¼
illustration board and chalk
e-math 9 by Oronce and Mendoza pp: 2310-315
Simplified Math for Grade 9 pp: 111- 112
References
Teacher’s Guide Pages
Learner’s Material pages

Other Learning Resources
https://www.slideshare.net/mobile/lorne27/similaritiesin-right-triangle
III. PROCEDURE
1. Preliminaries
a. Opening Prayer
b. Checking of Attendance
c. Cleaning the classroom before the lesson proper
d. Recapitulation /Review of past lesson
Teacher’s Activity
2. Motivation
Learner’s Activity
Look at the figure I post on the board.
Students do so..
R
N
S
A
Y
I
What do you see?
How many triangles do you see?
I see many triangles.
Are you sure?
4 maám!
Okay, can you name all 4 triangles?
Yes maám!
RNS
SYI
NAY
Very good!
Out of that figure you see 4 triangles!
What type of triangle is
RAY ?
RAY
Right triangle maám!
That’s right!
3. Lesson Proper
A. Engage
For today, kindly read first the
following lesson objectives I show on
the slide.
Students read the learning
objectives:
a. prove the Right Triangle
similarity theorem; b.
determine similar right
triangles inscribed in a larger
triangle;
c. find the length of an altitude
and leg of right triangle using
geometric mean
Okay class, I hope you are ready for our
lesson today.
Yes ma’am!
Pay attention and participate actively. I
have here strip of award that is
equivalent to your recitation today, The
more you participate, the more strips
of award you will get.
Alright?
Yes maám!
What triangle do you see?
The same with
figure.
RAY you saw in the Right Triangle ma’am!
Why do you call it Right triangle?
Yes maám!
Because one angle is 90◦.
Very good!
What are the different parts of right
triangle?
Yes right, Two legs are shorter than
hypotenuse.
There are two legs, and a
hypotenuse.
Let’s name the triangle ABC.
C
A
D
B
Students look at the figure.
By point plotting theorem we draw a
line from angle C to the hypotenuse and
name this segment CD.
Do you know what is this segment
called?
Altitude maám!
What is an altitude class?
Altitude is the length from the
vertex of a right angle to the
hypotenuse.
Right!
What do you observe to the right
triangle?
The altitude divides the
triangle into two smaller right
triangles.
That’s good observation!
C
A
D
B
Name the triangles formed?
That’s correct!
Triangle CDB
And Triangle CDA
How about the original or the largest
triangle?
Triangle ABC
How many triangles do we form?
Three!
Absolutely!
We have now Three triangles after
flipping the other triangle vertically
and move the smallest triangle away
from the original triangle.
Look at the figures below.
A
A
C
B
Students look at the figure..
D
C
C
D
B
Do you see a small, medium and large
triangle?
Do you see similar triangles?
Yes ma’am!
Yes ma’am!
What do you think is our topic today?
Similarity of Right triangle.
That’s right!
C
B. Explore
Go back to the figure.
A
D
B
Do you have any idea what similarity
of right triangle theorem is?
Right Triangle Similarity
Theorem
The altitude to the hypotenuse of
a right triangle divides the
triangle into two triangles that
are similar to the original triangle
and to each other.
Very good!
When an altitude divides the triangle
into two to triangles, those two
triangles are similar to the original
and to each other.
Do you get it class?
Yes ma’am!
Let’s pair two triangles to each
other.
1. SMALL AND MEDIUM
A
D
C
C
D
Give the similar triangles,
Students listen attentively..
B
ADC ~
CDB
2. MEDIUM AND LARGE
A
A
D
C C
B
Give the similar triangles,
ADC ~
ACB
3. LARGE AND SMALL
A
C
D
B C
B
Give the similar triangles,
CDB ~
How many pairs of similar triangles
do we form?
ACB
Three!!!
Yes ma’am!
Is it clear now?
Alright,
Here is another theorem,
Geometric Mean-Altitude
Theorem 1
C. Explain
The altitude from the vertex of
the right angle of a right
triangle to its hypotenuse is the
geometric mean between the
lengths of the two segments
and the hypotenuse.
C
A
D
B
Let’s go back to the figure a
while ago.
What segment is the altitude
again?
How do we measure the
altitude of a right triangle?
Altitude is Segment CD.
Students think of how the altitude will
be measured.
The theorem says the altitude is
the geometric men between the
lengths of the two segments
Yes ma’am!
and the hypotenuse.
What is geometric mean?
The geometric mean of two positive
numbers a and b is the positive
𝒂 𝒙
number x that satisfies
=
𝒙 𝒃
That’s right, and we will be
using geometric mean to get
the length of the altitude
according to the theorem.
So, x² = ab , x =√𝑎𝑏
C
h
What is the formula?
A
D
𝐴𝐷
For example,
AD = 9ft
DB = 4ft
h=?
Therefore the length of the
altitude is 6ft
𝐶𝐷
=
𝐶𝐷 𝐵𝐷
CD = √𝐴𝐷( 𝐷𝐵 )
h = √9 (4)
= √36
=6
That’s correct!
Another example,
If AD = 10ft
And DB= 4ft
What is the value of the
altitude?
h = √10(4)
= √40
= 2√10
Or 6.32ft
B
Very good!
The next theorem is Geometric
Mean-Altitude Theorem 2.
Kindly read the statement..
Go back to the figure again..
Students read..
Geometric Mean-Altitude Theorem
2
If the altitude is drawn to the
hypotenuse of a right triangle, then the
lengths of each leg of the triangle is the
geometric mean between the legs of
the hypotenuse and the segment of the
hypotenuse adjacent to the leg.
Students look at the figure again.
C
h
A
D
B
AC is the leg adjacent to segment AD
What leg is adjacent to segment
AD?

Based from the theorem, the
geometric mean formula of
each leg ?
What leg is adjacent to segment
BD?
Example;
If AD = 9ft
DB= 4ft
AB = 13ft
𝐴𝐷
𝐴𝐶
𝐴𝐶
= 𝐴𝐵
AC = √𝐴𝐷(𝐴𝐵)
BC is the leg adjacent to segment BD
𝐷𝐵 𝐵𝐶
 𝐵𝐶 = 𝐴𝐵
BC = √𝐷𝐵 (𝐴𝐵)
AC = √(9)(13)
=√117
or 10.82 ft
Find AC and BC..
BC = √𝐵𝐷(𝐴𝐵)
= √4(13)
=√52
Or 7.21ft
Very good class!
D. Elaborate
Consider the figure;
Students look at the figure.
a
h
b
m
n
c
If m = 8,
n = 12,
c = 20
Find the value of h, a and b
Students’answers:
h =√𝑚𝑛
= √(12)(8)
= √(96)
Who wants to solve on the
board?
= 4√6
Or 9.8
a =√𝑚𝑐
= √(8)(20)
=√(160)
= 4√10
Or 12.65
b =√𝑛𝑐
= √(12)(20)
= √240
=4√15
Or 15.5
Good job!
Again, what does right triangle
similarity theorem state again?
How many triangles do we
form when an altitude is drawn
from the vertex of the right
angle of the right triangle?
The altitude to the hypotenuse of a
right triangle divides the triangle into
two triangles that are similar to the
original triangle and to each other.
Three!
And there are two geometricaltitude theorems, what are
those?
The altitude from the vertex of the
right angle of a right triangle to its
hypotenuse is the geometric mean
between the lengths of the two
segments and the hypotenuse.
If the altitude is drawn to the
hypotenuse of a right triangle, then the
lengths of each leg of the triangle is the
geometric mean between the legs of
the hypotenuse and the segment of the
hypotenuse adjacent to the leg.
Don’t forget that class!
E. Evaluate
Yes maám!
Group yourselves into 4. This activity is
a form of game.
Try to solve each problem I will be
posting as quickly as you can.
Students group themselves….
You will use an illustration board and a
chalk to write your answer.
I will press the bell when time is up and
whichever group gets the right answer
will get a point.
The group who gets the higher number
of points will be declared winner.
Do you get it class?
Yes maám!
Your time starts now….
1.
Students answers:
1. ) 24- 10 = 14
x = √14(10)
= √140
=2√35
Or 11.83ft
y = √(10)(24)
=√240
= 4√15
Or 15.5
2.
2.)
AP = √3(8)
= √24
=2√6
Or 4.9
AR= √3(11)
= √33
= 5.74
RE =3 + 8
= 11
AE = √8(11)
=√88
= 2√22
Or 9.38
Thank you maám!
And the group who gets the highest
points is group number……1 (sample
winner group)
Congratulations!
Go back to your seat and prepare for a
short quiz
Students do so..
IV. EVALUATION
On a ½ cross-wise, answer the following:
Using the figure below;
a. determine the three similar triangles;
b. find the value of x and y.
E
2ft
y
x
D
10
F
8 ft
G
V. ASSIGNMENT
February 28, 2020
Find the height of the roof:
1. A roof has a cross-section that is right angle.
The diagram shows the approximate
dimensions of this cross section.
A. Identify the similar triangles
B. Find the height of the roof.
2. State special right triangle theorems.
Reference: Any Geometry book
Prepared by:
FRANCIA P. FLORECE
Student Teacher
Verified by:
SUSAN T. ABINAL
Cooperating Teacher