Detailed Lesson Plan in Mathematics 7
I. OBJECTIVES
At the end of the lesson, the students should be able to:
1. Prove the Pythagorean theorem using dissection or cut out.
2. Solve problems involving the use of Pythagorean theorem.
3. Appreciate the use of Pythagorean theorem in real life.
II. SUBJECT MATTER
A. Topic
Pythagorean Theorem
B. References
 Orines, F., Manalo, C., Suzara, J. & Mercado, J. (2017). Next Century
Mathematics 7 (2nd ed.). Phoenix Publishing House,Inc.
 Woo, E. (2019, February 6). Pythagora’s Theorem (2 of 3: Dissection
Proof).Youtube.https://www.youtube.com/watch?v=EzCWuNZpBaQ&t=3s
 https://www.nuffieldfoundation.org
III. TOOLS AND MATERIALS
 Blackboard
 Chalk
 Television
 Visual Aids
IV. PROCEDURE
Teacher’s Activity
A. Preparatory Activities
1. Prayer
2. Greetings
3. Classroom inspection
4. Checking of attendance
5. Review
What is our previous lesson all about?
What is the Triangle Inequality Theorem?
Can you give me an example of a triangle by
giving the length of its three sides?
How can you say that it is a triangle?
Very good.
Student’s Activity
It is about Triangle Inequality
Theorem.
Triangle Inequality Theorem
states that in any triangle, the sum
of the lengths of any two of its
sides is greater than the length of
its third side.
8cm, 7cm and 3 cm
It is a triangle because when we
add the length of its two sides, it
is greater than the length of the
third side. 8 + 7 >3, 8 + 3 > 7 and
7+3>8
B. Motivation
Before we start our lesson, let’s play a jigsaw
puzzle.We are going to complete the picture by
putting the pieces together.
(The teacher will call for students who will do the
jigsaw puzzle)
What shape has been formed based on the puzzle?
(Some students will complete the
picture by putting the pieces
together.)
It is a right triangle
That’s right, it is a right triangle.
What can you say about the sides of the right The length of the sides are given.
triangle?
If I make one side of the right triangle unknown,
No.
can you find its length without measuring it?
Today, I will teach you how to find an unknown
side of a right triangle using the Pythagorean
theorem.
C. Lesson Proper
Pythagorean Theorem is one of the most useful
theorems in geometry. It was named after
Pythagoras of Samos, a Greek mathematician and
philosopher, who is thought to have given the first
proof of the theorem around 500 B.C.
What is the Pythagorean theorem? Class, kindly
read.
Let’s investigate if it is true. Last time, I asked you
to create your own right triangle and bring it to the
class together with three pieces of construction
paper in different colors, pencil, ruler, tape, and
scissors.
Do you have them?
In any right triangle, the square of
the length of the hypotenuse is
equal to the sum of the lengths of
the two legs.
Yes, ma’am.
Since we made our own right triangle, it means that
yours is different from mine and from your (The students will follow the
classmates. Let’s start by naming the sides of the instructions of the teacher)
right triangle using the alphabet in increasing
order. The shortest side will be a, the next one will
be b and the hypotenuse will be c.
Next, Let’s square the three sides of the right
triangle. To do that, let’s first measure the length
of side a. Then, using that length, make a square in
one of your construction papers. Be careful in
using your scissors. You will have something like
this. You will do the same thing for side b and side
c. Use different construction paper for it.
According to Pythagorean theorem, 2 + 2 = 2
To know if it is true, let’s combine 2 and 2 . to do
that, I want you to form your figures like this.
Then,using your ruler, draw a vertical line along
the right side of 2 . Next, draw a horizontal line in
2 that is aligned to the right corner of 2.
Lastly, name the parts we did in 2 using numbers.
Now, let’s cut 2 into the lines we drew. Like a
puzzle, we are going to arrange 2 and the parts of
2 on the top of 2.
If you notice that the pieces fit perfectly on the top
of 2 . It means that the sum of 2𝑎 2 is equal to 2 . If
you still have doubts, we can
separate the figures, then both measure their
length to know if they are equal.
Are the sum of your 2𝑎 2 equal to your 2?
Yes, ma’am.
What about you?
What about the whole class?
Yes, ma’am.
Yes, ma’am.
Just like what I said earlier, we can use the
Pythagorean theorem in finding the unknown side
of the right triangle.
Let me show you by using the right triangle of your
classmate as an example. Give me the length of the
two sides of your right triangle. Yes?
b = 4 and c = 5
Then using the Pythagorean theorem, I will solve
for the length of the third side. Then you confirm
it if it is correct.
2+2
=
a=
a=
a=
a=
a=3
2
2
=2
−2
2−2
(5)2 − (4)2
25 − 16
9
Now, let’s have some real life examples that use
the Pythagorean theorem.
1. A man goes 18 m due east and then 24 m due
north. Find the distance of his current position
from the starting point?
2+2
=2
c
c = (18)2 + (24)2
= 324 + 576
=
900
c = 30 m
Let’s have the second example.
2. A 25-foot ladder resting 7 feet from the base of
a building leans against it. How high does it reach
up the wall of the building?
Who wants to try it on the board? Yes?
2+2
=2
b=
b = (25)2 − (7)2
b = 625 − 49
b = 576
b = 24 ft
D. Generalization
What have you learned in today’s lesson?
What is the Pythagorean equation?
How do we use the Pythagorean theorem?
Very good class.
I learned about the Pythagorean
theorem.
2+2=2
We can use the Pythagorean
theorem in finding the unknown
side of a right triangle.
Application
Answer each problem for 1 minute on 1/4 sheet of paper. In every problem, the students
who will give the right answer will get 3 points each. While the first 3, will get 5 points.
The student who presents his/her answer on the board will get another 3 points.
1. A square garden has side 100 feet long. You want to build a brick path along a
diagonal of the square. How long will the path be?
2. A ladder 40 feet long is placed so that it will reach a window 32 feet high on one side
of a street. If it is turned over, its foot being held in position it will reach a window 24
feet high on the other side of the street. How wide is the street from building to building?
Answers
1.
2+2
=2
2=2+2
c= 2+2
c = (100)2 + (100)2
= 10000 + 10000
=
20000
= 141.4213562 ft.
= 141.42 ft.
2.
2+2
=2
2 =2−2
a=
a = (40)2 − (32)2
a = 1600 − 1024
a = 576
a = 24ft.
12
+ 12 = 2
12 = 2 - 12
1
=
2− 2
1
a+1
24 + 32
=56 ft.
=
(40)2 − (24)2
1600 − 576
1=
1024
1=
1 = 32 ft.
1
Evaluation
Illustrate and answer the following problems on a one whole sheet of paper for 5 minutes.
1. A ladder 13 m long is placed on the ground in such a way that it touches the top of a
vertical wall 12 m high. Find the distance of the foot of the ladder from the bottom of the
wall.
2. Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.
3.The height of two buildings is 34 m and 29 m respectively. If the distance between the
two buildings is 12 m, find the distance between their tops.
Assignment
Illustrate and answer the following problems in student’s mathematics notebook.
1. A mast is supported by two cables attached to the top, and to points on the ground 20
m from its base. The height of the mast is 30 m. Calculate the length of each cable.
2. A gate is strengthened by fixing a strut along each of its diagonals. The gate is 2 m
long and 1.2 m high. Find the length of each strut.
3. A tent is 2.8 m wide. Its sloping sides are 2.4 m long. Calculate the height of the tent.