1. I.
Objective
At the end of the lesson, at least 85% of students will be able to:
a. Derive the Pythagorean theorem
b. Solve different problem involving Pythagorean
c. Show enthusiasm on solving Pythagorean Theorem
II.
Subject Matter
Topic: Pythagorean Theorem
Reference: Geometry Metric Edition
Pages: 345 – 347
Materials: Projector, whiteboard
III.
Procedure
Teacher’s Activity
Students Activity

2. A. Preparation
1. Daily Routine
a. Greeting
Good morning class!
Good Morning ma’am, sir
b. Prayer
Let us pray
Our most gracious heavenly father, we thank you
for this new day. Lord may you bless us to
understand our new topic and we can apply it in
real life situation. All these we pray in Jesus name.
Amen.
c. Attendance
Miss Secretary is there anyone
absent today?
None, ma’am, sir.
2. Review
Class what topic did we
discussed yesterday?
Okay, thank you very much
The topic we discussed yesterday is all about
area of polygon

3. 3. Motivation
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B. Discussion
1. Lesson Proper
(For the activity had done, it will
connect to the new topic.)
Pythagorean theorem is a
relationship between the sides of a
right triangle. A right
is any
triangle that has one right internal
angle.
90ᵒ
Right angle
Pythagoras is the proponent of Pythagorean
theorem. He also stated that, in a right
triangle, the square of the hypotenuse is equal
to the squares of the two legs. That statement
implies
b
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4. c
c² = a² + b²
the Pythagorean only applies to a
right triangle only,
b
a
a
b
c
c
b
a
c
c
a
b
Class, did you know the area of the
big square is (a + b) ². The area of
triangles is 4( ) and the area of
the inner squares is c². to arranged
these, we have (a + b) = 4 ◦ ( ) +
c²

5. To simplify, first step (a + b) ² is a
binomial, we multiply
a² + 2ab + b² = 2ab + c²
(transposition cancellation)
a² + 2ab – 2ab + b² = c²
= a² + b² = c²
Let’s try some examples.
Solution: c =
Given: a =6, b =8, c =?
c=
c=
c=
c = 10
Thank you, it’s correct.
What if one leg of a triangle is
missing? In that case deriving of
formula again.
a² + b² = c²

6. = a² = c² + b² (getting one leg)
c² = a² + b²
-b² = a² - c²
-1
Divide the whole equation by -1
To omit the negative sign.
b² = -a² + c²
or
b² = a² - c²
Now, let’s apply Pythagorean Theorem to
problem solving.
A 4 meter ladder is 2m from the base of a
building. How high up does the ladder reach?
Solution:
x =4m
b² = a² - c²
z =?
z=
z=
y =2m
=
=
2. Application
Complete the table. Use the
Pythagorean relation in finding the
missing lengths.
z=2
m or 3.46 m

7. c
b
a
a
b
c
5
8
6
10
5
25
10
3.)
4.)
12
1.)
2.)
3. Generalization
Anyone who can state and
define Pythagorean Theorem?
Pythagorean Theorem is a mathematical
relationship between the sides of a right triangle.
A right triangle is any triangle that has one right
internal angle and Pythagoras stated, if the length
of legs (smallest side) are squared and their sum
is found, the sum will be equal to the square of the
longest side (hypotenuse).
4. Evaluation
Now, class please get a ½
sheet of paper and answer this.

8. 1.
c=
c=
c=
2.
c=
54
c = 13
26
?
b=
IV.
Assignment
b=
b=
b=
b = 47.33
3. Study about altitude and hypotenuse