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DETAILED LESSON PLAN IN MATHEMATICS MATHEMATICS 9 Solving a right triangle given the two legs and find the missing leg using the Pythagorean Theorem.
I-OBJECTIVES At the end of the lesson, lesson, the student should be able able to: a. Derive the Pythagorean Theorem b. Solve different problem involving Pythagorean Theorem c. Show c. Show enthusiasm on solving Pythagorean Theorem II-SUBJECT MATTERS a. Topic: Pythagorean Theorem b. References: K to 12 Grade 9 Mathematics (Learners Material) c. Materials: Power Point presentation, chalk board, projector
III-PROCEDURE
Teacher’ s Activity
Learner’s Activity
A. Preparatory Preparatory Activities Activities 1.Review Good morning class!
Good morning Ma’am!
How are you today?
We are fine Ma’am
That’s good to hear.
Okay class before we start. Our new lesson today, lets pray first Who will lead the prayer today? Theresa lead the prayer.
Ma’am Theresa Prayer…. Prayer…. Amen
Amen. Okay! Okay! Once again Good morning morning class!
Who is absent today? That’s good to hear all of you are present today.
Okay class, class, let’s have first a review before
None Ma’am
We move to the our new lesson. What was
Raising their hand.
our topic yesterday? Mel
Kinds of Triangle Ma’am.
Very good Mel!
Yes our topic yesterday is triangles. So give one example and draw it on the
Raising their hands.
board. Jerick
Acute triangle (the student draw an example of an acute triangle).
Acute triangle
What kind of triangle of this? Yes, Melissa.
Raising their hands. Obtuse triangle Ma’am!
Very Good Melissa.
Now let us move on to the third types of a triangle.
The Right triangle Do you have an idea about a right triangle?
Not yet Ma’am!
Have you heard it before?
2. Motivation Before we proceed to our discussion let’ s have a game called “Crossword Puzzle” I will divide the class into four (4) groups. the class into four (4) groups. Each groups will have five (5) representatives. You are going to cross out to the puzzle word.
Game…. Game…. Game….
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3.Discussion (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.
Right angle 90° 90°
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 two legs. That statement implies. b
a
c
c 2= a 2 + b 2 The Pythagorean only applies to a right triangle only.
b
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c
c
b
b
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a
a
b
Class did you know the area of the big square a b
is (a+b)2. The area of triangle is 4( 2 ) and the area of the inner squares is c 2. To a b
arranged these we have (a+b)=4, ( 2 )+c2
To simplify, first step (a+b) 2 is a binomial, we multiply. a2+2ab+b2 = 2ab+c2 a2+2ab-2ab+b 2 = c2 a2+b2 = c2
Let’s try some examples Given: a = 6, b = 8, c = ?
Solution : c =
√ +
c=
√ 6 + 8
c = √ 3 6+64 c = √ 100 Thank you its correct.
What if one leg of a triangle is missing? In that case deriving of formula again a2+b2=c2 a2+b2=c2 (getting one leg) b2=c2-a2 Now, let’s apply the Pythagorean Theorem to problem solving. A 4meter ladder is 2meter from the base of a building. How high up does the ladder reach?
c = 10
Solution: b2=c2-a2 c = 4m
b=?
b=
√ −
a = 2m
b = (4) −(2) b = (16) − (4) b = √12 b = 2√ 3 3.46
B. Past Lesson Proper 1. Generalization Again, what is our topic?
Raising their hands.
Rhea
Ma’am our topic for today is all about Pythagorean Theorem and how to find the missing leg of the right triangle.
Very Good Rhea! How about our formula? Yes, Rejoice
Raising their hands. Ma’am c 2 = a 2 + b 2
Very Good!
Class, how to solve or what are the steps to
Raising their hands.
solve the problem using the formula?
Ma’am first find what are given, what is
Rizza?
the missing leg, substitute the given on
Excellence Rizza!
the formula and solve it.
Very Good class, you already understand our Lesson for today.
2. Values infusion a. Fixing Skills Group the class into four and let them to
Complete the table and let them to complete
the table and solve the missing part of the right triangle. Use the Pythagorean Theorem.
c
b
a
a
5
b
8
6
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10
25
5
10
3)
4)
12
1)
2)
IV-EVALUATION Now, class please get a 1/2 sheet of paper and answer this
