Republic of the Philippines

Tuguegarao City Science High School

MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

DETAILED LESSON PLAN

IN
MATHEMATICS 9

Prepared by:
ALEXANDRA P. TANGAN
Practice Teacher

Checked by:
ARLON MACARUBBO
Resource Teacher
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

Detailed Lesson Plan in Math

Mathematics 9
Quarter 4

I. Learning Objectives
At the end of the lesson, the students should be able to:
a. Identify the properties that make a quadrilateral a parallelogram,
b. Prove that a given quadrilateral is a parallelogram using the properties, and
c. appreciate the importance of geometric properties in real-life application.

II. Subject Matter

A. Topic: Determine the Conditions That Make a Quadrilateral a Parallelogram
B. Instructional Materials: PowerPoint presentation, whiteboard marker, printed IMs and printed worksheets
C. References: M9GE-IIIa-2, YouTube
III. Learning Procedures
Teacher’s Activity Student’s Activity

A. PREPARATION

Opening Prayer

May I ask everyone to pause for a while and feel the

presence of the Lord for the opening Prayer.

One student will lead the prayer.

Greetings
Good morning/Afternoon Class!
Good morning, Ma’am!

Checking of Attendance
Is there anyone who is absent today class?

None, Ma’am!
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

B. MOTIVATION

Before we begin with our discussion for today, we

will have an activity titled, “MATHriddle Me”. Here
are the mechanics of the activity:
I. The class will be divided into two
groups, each with a board along with a
marker.
II. A math riddle will be flashed on the
screen.
III. The class will guess the answer, and they
will raise their boards when the time is
up.
IV. The group that has the higher score will
win.

Are you ready?

Yes Ma’am!

The game will start.

C. PRESENTATION
Let’s give everyone a round of applause. The
matches and definitions are all correct. From that
activity, what do you think will be our lesson for
today?

Ma’am, properties that revolves around properties of

That is correct! However, before delving in our parallelogram.
topic, let us first read the learning objectives for
today. Everyone, please read:

At the end of the lesson, the students should be able

to:

a. Define the properties that make a

quadrilateral a parallelogram,
b. determine the conditions that make a
quadrilateral a parallelogram, and
c. appreciate the importance of geometric
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

That is correct! Now, can anyone give me the

definition of a quadrilateral?

Ma’am, a quadrilateral is a polygon with four sides.

Absolutely right! How about a parallelogram?

Ma’am it is a quadrilateral with opposite side equal

So, are all parallelogram quadrilaterals? Why? and parallel.

Yes Ma’am because parallelogram is a type of

quadrilateral since by definition it has four sides.
How about quadrilaterals? Are all quadrilateral
parallelograms? Why?
No Ma’am because there are some quadrilaterals that
do not have the defining properties of a parallelogram
like the kite and trapezoids.
That’s all true! A parallelogram is a special type of
quadrilateral with unique properties. There are five
key conditions that will help us determine whether a
given quadrilateral is a parallelogram. Let’s start by
examining the first condition:
I. A quadrilateral is a parallelogram if its
opposite sides are congruent. Please read.

- if the opposite sides of a quadrilateral have equal

lengths, then it must be a parallelogram.

QU ≅ DA
QD ≅ UA

Example:
1. CUTE is a quadrilateral. Determine the length of
UT that will make CUTE a parallelogram.

CE ≅ UT
8 cm=UT
Therefore, UT must be 8cm to make CUTE a
parallelogram.

2. CUTE is a quadrilateral. Determine the value of x

 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

that will make CUTE a parallelogram.

ET ≅ CU
x +7=12
x=12−7
x=5
Therefore, x must be 5 units to make CUTE a
parallelogram.

That’s correct! Now, let’s proceed to the 2nd

condition:
II. A quadrilateral is a parallelogram if both pairs - if both pairs of the opposite angles have the same
of opposite angles are congruent. Please read. measure, then it must be a parallelogram.

∠Q ≅ ∠ A
∠U ≅ ∠ D

Example:
1. CUTE is a quadrilateral. Determine the length of
∠ E that will make CUTE a parallelogram.

∠ E ≅ ∠U
∠ E ≅ 50 °
2. CUTE is a quadrilateral. Determine the value of x
Therefore, ∠ E must be 50 ° to make CUTE a
that will make CUTE a parallelogram.
parallelogram.
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

∠T ≅ ∠C
4 x 120
=
4 4
x = 30
Therefore, x must be 30 to make CUTE a
parallelogram.
III. A quadrilateral is a parallelogram if any pair
of consecutive angles are supplementary. Please
read.
- if any two consecutive angles add up to 180 ° , then
it must be a parallelogram.

m ∠ Q+ m∠ U =180 °
m ∠ U +m∠ A=180 °
m ∠ A +m∠ D=180 °
m ∠ D+ m∠ Q=180°

Example:
1. CUTE is a quadrilateral. Determine m ∠ U that
will make CUTE a parallelogram.

m ∠ U + m ∠ T=180°
m ∠ U + 100°=180 °
m ∠ U =180 °=100 °
m ∠ U =80 °
Therefore, ∠ U must be 80 ° to make CUTE a
parallelogram.

IV. A quadrilateral is a parallelogram if the

diagonals bisect each other.

QO ≅ AO
DO ≅ UO

Example:
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

CUTE is a quadrilateral with diagonals CT and UE

Intersecting at point O. Determine the length of OT
that will make CUTE a parallelogram.

OT ≅ OC
OT =5 m
Therefore, OT must be 5m to make CUTE a
quadrilateral.

V. A quadrilateral is a parallelogram if each

diagonal divides the parallelogram into two
congruent triangles.
Δ QDA ≅ ΔAUQ

Remember that the correct order of the sides when

naming a triangle is important. You should follow
certain arrangement, which can be derived from
when a transversal cuts parallel lines. Then, we can
further say the alternate interior angles are
congruent.
QD ≅ AU
DA ≅ UQ
AQ ≅ QA

Example:
CUTE is a quadrilateral. Name the triangle that is
congruent to ΔUCE that will make CUTE a
parallelogram.

ΔUCE ≅ ΔETU
Therefore, ΔETU must be congruent to ΔUCE to
make CUTE a parallelogram.

D. Generalization
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

Those are absolutely correct! Again, let’s review

what we tackled today. Is the difference between a
parallelogram and a quadrilateral??
Ma’am, a quadrilateral is a polygon with four sides,
while a parallelogram is a type of quadrilateral since,
by definition, it has four sides; however, its opposite
sides are equal and parallel. Also, all parallelograms
are quadrilaterals but not all quadrilaterals are
parallelograms.
That’s right. Now, what are the conditions that make
a quadrilateral a parallelogram?
Ma’am the conditions that makes a quadrilateral a
parallelogram are as follows:
I. A quadrilateral is a parallelogram if its
opposite sides are congruent.
II. A quadrilateral is a parallelogram if both pairs
of opposite angles are congruent
III. A quadrilateral is a parallelogram if any pair
of consecutive angles are supplementary.
IV. A quadrilateral is a parallelogram if the
diagonals bisect each other.
V. A quadrilateral is a parallelogram if each
diagonal divides the parallelogram into two
congruent triangles.

E. Application
Very good! Please bear in mind those conditions to
determine whether a given quadrilateral is a
parallelogram. Now, let’s move on to the usefulness
of what we tackled. What do you think is its
significance? Ma’am learning about the different conditions is
essential for us to solve problems related to sides and
angles within a parallelogram.

That is indeed correct! It seems that you did

understand our topic today. That ends our lesson for
today. Goodbye, class! Goodbye, Ma’am!

IV. EVALUATION:
A. Refer to the given figure and answer the following.

MATH is a parallelogram
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

1. If MT = 15, then AH = _____

2. If m ∠ A =60 ° , then m ∠ H=¿______
3. If m ∠ H =95 ° , then m ∠ M =¿¿
4. If AT = 30, then PA = ______
5. If PH = 9, then MH = ______

V. ASSIGNMENT
Create a simple drawing of an object that uses parallelograms and label its features.
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________