UNIVERSITY OF CAGAYAN VALLEY
Victor V. Perez Campus, Tuguegarao City
Detailed
Lesson Plan
In
Grade 9 Mathematics
Prepared by:
LESLY L. EYAM
Mentee
Checked by:
GRACE G. CUSIPAG
Mentor
UNIVERSITY OF CAGAYAN VALLEY
Victor V. Perez Campus, Tuguegarao City
I. OBJECTIVES:
At the end of the discussion, the students should be able to:
a. State the theorems on rectangle;
b. Apply the theorems on rectangle in solving problems; and
c. Relate theorems on rectangle in real life situation.
II.
SUBJECT MATTER:
TOPIC: Special Parallelogram (THEOREM ON RECTANGLE)
REFERENCE: Q3_ Mathematics 9_ Module 2
MATERIALS: Laptop, power point presentation, television, chalk and eraser.
VALUE INTEGRATION: Cooperation and understanding
III. PROCEDURE:
TEACHERS ACTIVITY
STUDENTS ACTIVITY
Daily Routine
Good morning class!
May we all stand and feel the presence of the
Lord.
Good morning, Ma’am!
Our father who art in heaven …..
Before you take your sit kindly pick up any
litters under your chairs and aligned your chairs.
Anyone who is absent today?
A. MOTIVATION
Before we start our discussion, let’s have an
activity first. This activity is called, “3 pics 1
math word”.
1.
2.
None ma’am.
UNIVERSITY OF CAGAYAN VALLEY
Victor V. Perez Campus, Tuguegarao City
3.
1. RECTANGLE
2. THEOREM
3. PARALLELOGRAM
B. PRESENTATION
Based on the activity, do you have any idea
on what will be our topic for today? Yes Bj?
Any idea carmela?
Very Good!
Our topic for today is all about theorems on
the different kinds of parallelograms.
But today we are going to focus on the theorems
of rectangle.
Here’s the objectives of our lesson for today.
C. LESSON PROPER
First, who can give me the different kinds of
parallelogram?
Very Good!
We call this also a special parallelogram.
So, let’s start with the theorem of rectangles.
Let’s define first what is theorem and describe a
rectangle.
Who can describe a rectangle?
Very Good!
How about theorem? Anyone?
Very good!
What are the properties of rectangle? Who
can give one? Next?
Parallelogram.
I think our topic today is all about theorem
ma’am.
First, state the theorems on rectangle;
Second, apply theorem on rectangle in
solving problems; and
Lastly, apply the theorems in real life
situation.
Rectangle, rhombus and square.
A rectangle is a parallelogram with four
right angles.
Theorem is a mathematical statement that
can be proved.
1. Opposite sides are parallel and
congruent.
2. Opposite angles are congruent and
supplementary.
3. All four angles are right angles.
4. Consecutive
angles
are
supplementary
5. Diagonals bisect each other and are
congruent
6. Each diagonal separates the
rectangle into two congruent
triangles.
UNIVERSITY OF CAGAYAN VALLEY
Victor V. Perez Campus, Tuguegarao City
Theorem 1.
If a parallelogram has a right angle, then it
has four right angles and the parallelogram is a
rectangle.
Given:
WINS is a rectangle with W is a right angle.
Who wants to draw the figure?
Very Good!
So, we are going to prove that our I, N and S
are right angles.
Proof:
STATEMENTS
1. WINS is a rectangle with
W is a right angle.
REASONS
1.Given
STATEMENTS
REASONS
2. W = 90
3.  W ≌ N and I ≌S
Since, number 2 and 3, statements are given, so
who can give me the reasons?
Very Good!
STATEMENTS
REASONS
4. W = mN
m I = m S
5. m N = 90
6. m W + m I = 180
Who can give me the reason in number 4?
How about number 5?
And number 6?
Very Good!
STATEMENTS
7. 90 + m I = 180
8. 90 = 90
9. W = 90
10.. mS = 90
11.  I, N, and S
are right angles.
12. WINS
rectangle
is
a
REASONS
7. Substitution
8.Reflexive property
9.Subtraction
property
10. Substitution
11. If the measure of
an angle is 90, then it
is a right angle.
12.Definition of a
rectangle
2. Definition of right angle.
3. In parallelogram, opposite angles are
congruent.
4. Definition of congruent angles.
5. Substitution
6. Consecutive angles are
supplementary.
UNIVERSITY OF CAGAYAN VALLEY
Victor V. Perez Campus, Tuguegarao City
Let’s proceed to theorem 2:
The diagonals of a rectangle are congruent.
Given:
̅.
WINS is a rectangle with diagonals ̅̅̅̅̅
𝑊𝑁 and 𝑆𝐼
̅
̅̅̅̅̅ ≌ 𝑆𝐼
Prove: 𝑊𝑁
Who can draw the figure?
So, let’s have the proof:
STATEMENTS
REASONS
1. WINS is a 1. Given
parallelogram with
Diagonals ̅̅̅̅̅
𝑊𝑁 and
𝑆𝐼
̅̅̅̅̅ ≌ 𝐼𝑁
̅̅̅̅
2.Opposite sides of a
2. 𝑊𝑆
parallelogram
are
congruent.
3.  WSN and m  3. If a parallelogram
INS
are
right has one right angle,
then it has four right
angles.
angles
and
the
parallelogram is a
rectangle.
4. All right angles are
4. WSN ≌  INS
congruent.
̅̅̅̅
̅̅̅̅
5.Reflexive property.
5. 𝑆𝑁 ≌ 𝑁𝑆
6.SAS
congruence
6. WSN ≌  INS
postulate
̅
̅̅̅̅̅ ≌ 𝑆𝐼
7. Diagonals of a
7. 𝑊𝑁
rectangle
are
congruent.
Who can draw the figure?
Now, let’s have an example:
1. Quadrilateral TALK is a rectangle. Find
̅̅ = 5x-4 and ̅̅̅̅̅
the value of x if ̅̅
𝑇𝐿
𝐾𝑀 =
2x+3.
So, this is the figure:
T
A
M
M
K
L
Since, the diagonals of a rectangle are congruent,
̅̅̅̅ ,
̅̅̅̅ = 𝐴𝐾
𝑇𝐿
Where, ̅̅̅̅
𝐴𝐾 = 2 ̅̅̅̅̅
𝐾𝑀
̅̅̅̅ = 2 𝐾𝑀
̅̅̅̅̅
Hence, 𝑇𝐿
5x-14 = 2(2x +3)
5x – 14 = 4x +6
W
S
I
N
UNIVERSITY OF CAGAYAN VALLEY
Victor V. Perez Campus, Tuguegarao City
5x-4x = 6+14
x = 20.
Please answer example;
2. Quadrilateral TALK is a rectangle. Find
̅̅ = 7x-16 and ̅̅̅̅̅
the value of x if ̅̅
𝑇𝐿
𝐾𝑀 =
3x+4.
Very Good!
Let’s proceed to activity.
Since, the diagonals of a rectangle are
̅̅̅ = ̅̅̅̅
congruent, ̅𝑇𝐿
𝐴𝐾 ,
̅̅̅̅
̅̅̅̅̅
Where, 𝐴𝐾 = 2 𝐾𝑀
̅̅̅̅ = 2 𝐾𝑀
̅̅̅̅̅
Hence, 𝑇𝐿
7x-16 = 2(3x+4)
7x-16 = 6x+8
7x- 6x = 8+16
x = 24
D. APPLICATION
Direction: Bring out one whole sheet of
paper and answer this activity. This activity is
called, “COMPLETE ME” You’re just to
complete this table.
Given:
̅.
̅̅̅̅̅ and 𝑆𝐼
WINS is a rectangle with diagonals 𝑊𝑁
̅
̅̅̅̅̅
Prove: 𝑊𝑁 ≌ 𝑆𝐼
STATEMENTS
1.
̅̅̅̅̅ ≌ 𝐼𝑁
̅̅̅̅
2. 𝑊𝑆
3.  WSN and m
 INS are right
angles.
4.
5. ̅̅̅̅
𝑆𝑁 ≌ ̅̅̅̅
𝑁𝑆
6.
REASONS
1. Given
2.
3.
4. All right angles
are congruent.
5.
6.SAS congruence
postulate
̅
7. ̅̅̅̅̅
𝑊𝑁 ≌ 𝑆𝐼
E. GENERALIZATION
Before we end up, let’s have a recap.
How many theorems we discuss under rectangle?
Very Good!
What is theorem again?
Possible answers:
1. WINS is a parallelogram with
Diagonals ̅̅̅̅̅
𝑊𝑁 and 𝑆𝐼
2. Opposite sides of a parallelogram are
congruent.
3. If a parallelogram has one right
angle, then it has four right angles
and the parallelogram is a rectangle.
4. WSN ≌  INS
5. Reflexive property.
6.  WSN ≌  INS
7. Diagonals of a rectangle are
congruent.
Two theorems ma’am.
It is a mathematical statement that can be
proven.
Very Good!
What are the theorems of rectangle that we have
discuss? Yes Jamaica?
Very Good!
Theorem 1.
If a parallelogram has a right angle,
then it has four right angles and the
parallelogram is a rectangle.
Theorem 2.
The diagonals of a rectangle are
congruent.
UNIVERSITY OF CAGAYAN VALLEY
Victor V. Perez Campus, Tuguegarao City
IV. EVALUATION:
Direction: Answer this in your notebook. (10 Points).
Use rectangle FRAT and the given information to answer each of the following.
F
R
Y
T
a.
b.
c.
d.
A
mFRT = 65. Find mTRA, mATR, and m RTF.
mFYT = 110. Find mYTF, mYFT, and mYFR.
mFRT = 70. Find mTRA, mATR, and mRTF.
mFYT = 105. Find mYTF, mYFT, and mYFR.
V. ASSIGNMENT:
̅̅̅̅ = 5x-14 and 𝐾𝑀
̅̅̅̅̅ = 2x+3.
A. Quadrilateral TALK is a rectangle. Find the value of x if 𝑇𝐿
B. Have an advance reading about the theorems on rhombus.