math region module

1. i
Mathematics Activity Sheet
Quarter 3 – MELC 1 & 2
Determining the Conditions That Make A
Quadrilateral A Parallelogram
Using Properties to Find Measures of Angles,
Sides and Other Quantities Involving
Parallelograms
9
REGION VI – WESTERN VISAYAS

2. ii
Development Team of Mathematics 9 Activity Sheet
Writer: Nancy P. Bascar
Illustrators: Jerome Jordan Z. Ponsica, Eldiardo E. de la Peña
Layout Artists: Antonio O. Rebutada, Mark Jairee G. Cabus
Schools Division Quality Assurance Team:
Prilyn S. Albarico
Gigi Sheila S. Villanueva
Romalyn B. Tomarong
Mary Ann C. Biaquis
Mae Joy M. Tan, PhD
Division of Escalante City Management Team:
Clarissa G. Zamora, CESO VI
Ermi V. Miranda, PhD
Jason R. Alpay
Lilibeth G. Langrio
Jean G. Pilongo
Regional Management Team
Ma. Gemma M. Ledesma
Pedro T. Escobarte, Jr.
Elena P. Gonzaga
Donald T. Genine
Adonis A. Mosquera - OIC
Mathematics Grade 9
Activity Sheet No. 1
First Edition, 2021
Published in the Philippines
By the Department of Education
Region 6 – Western Visayas
Republic Act 8293, section 176 states that: No copyright shall subsist in any
work of the Government of the Philippines. However, prior approval of the
government agency or office wherein the work is created shall be necessary for
exploitation of such work for profit. Such agency or office may, among other things,
impose as a condition the payment of royalties.
This Learning Activity Sheet is developed by DepEd Region 6 – Western
Visayas.
ALL RIGHTS RESERVED. No part of this learning resource may be
reproduced or transmitted in any form or by any means electronic or mechanical
without written permission from the DepEd Regional Office 6 – Western Visayas.

3. iii
Introductory Message
Welcome to Mathematics Grade 9!
The Learning Activity Sheet is a product of the collaborative efforts of the
Schools Division of Escalante City and DepEd Regional Office VI - Western Visayas
through the Curriculum and Learning Management Division (CLMD). This is
developed to guide the learning facilitators (teachers, parents and responsible adults)
in helping the learners meet the standards set by the K to 12 Basic Education
Curriculum.
The Learning Activity Sheet is self-directed instructional materials aimed to
guide the learners in accomplishing activities at their own pace and time using the
contextualized resources in the community. This will also assist the learners in
acquiring the lifelong learning skills, knowledge and attitudes for productivity and
employment.
For learning facilitator:
The Mathematics 9 Activity Sheet will help you facilitate the teaching-
learning activities specified in each Most Essential Learning Competency (MELC)
with minimal or no face-to-face encounter between you and learner. This will be
made available to the learners with the references/links to ease the independent
learning.
For the learner:
The Mathematics 9 Activity Sheet is developed to help you continue
learning even if you are not in school. This learning material provides you with
meaningful and engaging activities for independent learning. Being an active
learner, carefully read and understand the instructions then perform the activities
and answer the assessments. This will be returned to your facilitator on the agreed
schedule.

4. 1
Learning Activity Sheets (LAS) No. 1a
Name of Learner: _____________________________________________________
Grade and Section: _________________________ Date: _______________________
MATHEMATICS 9 ACTIVITY SHEET
Determining the Conditions That Make A
Quadrilateral A Parallelogram
I. Learning Competency with Code
• The learner determines the conditions that make a quadrilateral a
parallelogram.
M9GE-IIIa-2
II. Background Information for Learners
This Learning Activity Sheet focuses on determining the conditions that make
a quadrilateral a parallelogram. After which you will be able to determine the properties
of a parallelogram and use these to find measures of angles, sides, and other
quantities involving parallelograms.
A quadrilateral is a close plane figure consisting of four line segments or sides.
Examples of quadrilaterals are: Parallelogram, Rectangle, Square, Rhombus and kite.
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel.
The illustration below represents a parallelogram; both pairs of opposite side are
parallel and congruent, and opposite angles are congruent.
There are quadrilaterals that can be consider a parallelogram, following some
conditions. These are the following conditions that makes a quadrilateral a
parallelogram:
115.58°
115.58°
64.42°
64.42°
3.43cm
4.74cm
4.74cm
3.43cm
E
L
O V
Quarter 3, Week 1

5. 2
CONDITIONS THAT MAKE A QUADRILATERAL A PARALLELOGRAM
1. A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.
Study the illustration below.
In the figure, the pairs of opposite sides are 𝐴𝑅
̅̅̅̅ & 𝐶𝐸
̅̅̅̅; 𝐴𝐶
̅̅̅̅ & 𝑅𝐸
̅̅̅̅. Then,
measure of 𝐴𝑅
̅̅̅̅ = 6.40𝑐𝑚 𝑎𝑛𝑑 measure of 𝐶𝐸
̅̅̅̅ = 6.40𝑐𝑚; also measure of
𝐴𝐶
̅̅̅̅ = 3.43𝑐𝑚 𝑎𝑛𝑑 measure of 𝑅𝐸
̅̅̅̅ = 3.43𝑐𝑚. It shows that the pairs of opposite side
of CARE are congruent.
Therefore, quadrilateral CARE is a parallelogram.
The figure above clearly illustrates that a quadrilateral is a parallelogram if both
pairs of opposite sides are congruent.
2. A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.
Study the illustration below.
In the figure, the pairs of opposite angles are < 𝐴 𝑎𝑛𝑑 < 𝐻; < 𝑀 𝑎𝑛𝑑 < 𝑇.
Then, measure of < 𝐴 = 120° 𝑎𝑛𝑑 measure of < 𝐻 = 120°; also measure of
< 𝑀 = 60° and measure of < 𝑇 = 60°. It shows that the pairs of opposite angles of
MATH are congruent.
Therefore, quadrilateral MATH is a parallelogram.
The figure above clearly illustrates that a quadrilateral is a parallelogram if
both pairs of opposite angles are congruent.
3.43cm
6.40cm
6.40cm
3.43cm
E
C
A R
120°
60°
120°
60°
H
M
A
T

6. 3
3. A quadrilateral is a parallelogram if both pairs of consecutive angles are
supplementary.
Study the illustration below.
In the figure, the pairs of consecutive angles are < 𝐴 𝑎𝑛𝑑 < 𝑇; < 𝑇 𝑎𝑛𝑑 < 𝐻;
< 𝑀 𝑎𝑛𝑑 < 𝐻; < 𝐴 𝑎𝑛𝑑 < 𝑀. The measure of < 𝑀 = 60°; 𝑚 < 𝐴 = 120°;
𝑚 < 𝑇 = 60°; and 𝑚 < 𝐻 = 120°. If we are going to add the pairs of consecutive
angles the result are:
𝑚 < 𝐴 + 𝑚 < 𝑇 = 120° + 60° = 180°
𝑚 < 𝑇 + 𝑚 < 𝐻 = 60° + 120° = 180°
𝑚 < 𝑀 + 𝑚 < 𝐻 = 60° + 120° = 180°
𝑚 < 𝐴 + 𝑚 < 𝑀 = 120° + 60° = 180°, which is consider as supplementary.
Supplementary angles are two angles having a sum of 180°. It shows that pairs of
consecutive angles of MATH are supplementary.
Therefore, quadrilateral MATH is a parallelogram.
4. A quadrilateral is a parallelogram if the diagonals bisect each other.
A diagonal is a line segment joining two nonconsecutive vertices of a polygon.
Bisect means to divide into two equal parts.
A line segment bisects another line segment if it divides the segment into two
congruent parts.
Study the illustration below.
In the figure, the diagonals are 𝑊𝑅
̅̅̅̅̅ 𝑎𝑛𝑑 𝑂𝐷
̅̅̅̅ which intersect at point A. As the
two diagonals intersect at point A it forms a pair of segments. The pairs of segments
formed by intersecting diagonals are: 𝑂𝐴
̅̅̅̅ 𝑎𝑛𝑑 𝐷𝐴
̅̅̅̅; and 𝑊𝐴
̅̅̅̅̅ 𝑎𝑛𝑑 𝑅𝐴
̅̅̅̅. As shown in the
figure 𝑂𝐴
̅̅̅̅ ≅ 𝐷𝐴
̅̅̅̅ and 𝑊𝐴
̅̅̅̅̅ ≅ 𝑅𝐴
̅̅̅̅; so, diagonals 𝑊𝑅
̅̅̅̅̅ 𝑎𝑛𝑑 𝑂𝐷
̅̅̅̅ of WORD bisect
each other.
Therefore, quadrilateral WORD is a parallelogram.
120°
60°
120°
60°
H
M
A
T
2.83cm
4.12cm
4.12cm
2.83cm
A
D
W
O R

7. 4
E
R
S
R
O
S
5. A quadrilateral is a parallelogram if each diagonal divides a parallelogram into
two congruent triangles.
Two triangles are congruent if their corresponding sides are equal in length,
and their corresponding angles are equal in measure.
Study the illustration below.
In the figure, 𝑅𝑆
̅̅̅̅ is the diagonal of ROSE. It divides the quadrilaterals
into two triangles and those are ∆𝑅𝑂𝑆 𝑎𝑛𝑑 ∆𝑆𝐸𝑅. In the two triangles the pairs of
corresponding sides are 𝑂𝑅
̅̅̅̅ 𝑎𝑛𝑑 𝑆𝐸
̅̅̅̅; 𝑂𝑆
̅̅̅̅ 𝑎𝑛𝑑 𝐸𝑅
̅̅̅̅; 𝑅𝑆
̅̅̅̅ 𝑎𝑛𝑑 𝑆𝑅
̅̅̅̅ and they are all
congruent. As well as the pairs of corresponding angles are: ∠𝑅𝑆𝑂 𝑎𝑛𝑑 ∠𝑆𝑅𝐸;
∠𝑅𝑂𝑆 𝑎𝑛𝑑 ∠ 𝑆𝐸𝑅; ∠𝑅𝑆𝑂 𝑎𝑛𝑑 ∠𝑆𝑅𝐸 and they are also congruent. It shows that the
pairs of corresponding sides and corresponding angles are congruent, so
∆𝑅𝑂𝑆 𝑎𝑛𝑑 ∆𝑆𝐸𝑅 are congruent.
Therefore, quadrilateral ROSE is a parallelogram.
6. A quadrilateral is a parallelogram if one pair of opposite sides are both congruent
and parallel.
In the figure, the pair of opposite side of ROSE is 𝑂𝑆
̅̅̅̅ 𝑎𝑛𝑑 𝑅𝐸
̅̅̅̅ and they are
congruent and parallel.
Therefore, quadrilateral ROSE is a parallelogram.
E
R
O
S
E
R
O S

8. 5
III. Accompanying DepEd Textbook and Educational Sites
Mathematics 9 Learner’s Materials, First Edition, 2014, Merden L. Bryant,
Leonides E. Bulalayao, Melvin M. Callanta, Jerry D. Cruz, Richard F. De Vera,
Gilda T. Garcia, Sonia E. Javier, Roselle A. Lazaro, Bernadeth J. Mesterio, and
Rommel Hero A. Saladino
IV. Activity Proper
1. Directions / Instructions:
For further information about this lesson, please refer to Mathematics Learner’s
Material pages 309 - 314.
2. Exercises / Activities
Exercise 1: Complete me!
Direction: Fill in the blank the correct word to complete the conditions that makes a
Quadrilateral a Parallelogram.
1. A quadrilateral is a parallelogram if both pairs of ________________ sides
are ________________.
2. A quadrilateral is a parallelogram if both pairs of ________________ angles
are ________________.
3. A quadrilateral is a parallelogram if both pairs of ________________ angles
are ________________.
4. A quadrilateral is a parallelogram if the ___________________ bisect each
other.
5. A quadrilateral is a parallelogram if each _________________ divides a
parallelogram into two _______________________________.
6. A quadrilateral is a parallelogram if one pair of opposite sides are both
_____________ and _____________.
Exercise 2: Defense! Defense!
Directions: Study the following parallelograms below then determine what condition
that makes the figure a parallelogram.

9. 6
4.
3. Guide Questions
1. What is a quadrilateral?
2. What are the different kinds of quadrilaterals?
3. What is a parallelogram?
4. What are the different conditions that makes a quadrilateral a
parallelogram?
V. Reflection
Complete the statement.
I have learned that_______________________________________________
___________________________________________________________________.
I have realized that _____________________________________________
___________________________________________________________________.
I will apply _________________________________________________________________
_________________________________________________________________________________.
VI. Answer Key
Exercise
1:
Complete
me!
1.
Opposite;
congruent
2.
opposite;
congruent
3.
consecutive;
supplementary
4.
diagonals
5.
diagonals;
congruent
triangles
6.
parallel
and
congruent
Exercise
2:
DEFENSE!
DEFENSE!
1.
A
quadrilateral
is
a
parallelogram
if
both
pairs
of
opposite
sides
are
congruent.
2.
A
quadrilateral
is
a
parallelogram
if
both
pairs
of
opposite
angles
are
congruent.
3.
A
quadrilateral
is
a
parallelogram
if
the
diagonals
bisect
each
other.
4.
A
quadrilateral
is
a
parallelogram
if
each
diagonal
divides
a
parallelogram
into
two
congruent
triangles.

10. 7
Learning Activity Sheets (LAS) No. 1b
Name of Learner: _____________________________________________________
Grade and Section: _________________________ Date: _______________________
MATHEMATICS 9 ACTIVITY SHEET
Use Properties to Find Measures of Angles, Sides and
Other Quantities Involving Parallelograms
I. Learning Competency with Code
• The learner uses properties to find measures of angles, sides and other
quantities involving parallelograms.
M9GE-IIIb-1
II. Background Information for Learners
This Learning Activity Sheet focuses on using properties to find measures of
angles, sides and other quantities involving parallelograms. Properties of
parallelogram was developed through the conditions that makes quadrilateral a
parallelogram. These properties of a parallelogram can be used to find measures of
angles, sides, and other quantities involving parallelograms.
The following are the properties of parallelogram:
Properties of Parallelogram
1. In a parallelogram, any two opposite sides are congruent.
2. In a parallelogram, any two opposite angles are congruent.
3. In a parallelogram, any two consecutive angles are supplementary.
4. The diagonals of a parallelogram bisect each other.
5. A diagonal of a parallelogram forms two congruent triangles.
We are going to use these properties to find the measures of angles, sides, and other
quantities of a parallelogram.
Examples:
1. Given ABCD as shown below. Find the measure of side 𝐴𝐷
̅̅̅̅.
6.2cm
D
B
A
C
Quarter 3, Week 1

11. 8
Since the opposite side of 𝐴𝐷
̅̅̅̅ is 𝐵𝐶
̅̅̅̅. And measure of 𝐵𝐶
̅̅̅̅ = 6.2cm, therefore 𝑨𝑫
̅̅̅̅ =
6.2cm using parallelogram property 1.
2. Below is parallelogram ABCD. Consider each given information and answer
the questions that follow.
Given: 𝐴𝐵
̅̅̅̅ = (3x – 5)cm, 𝐵𝐶
̅̅̅̅ = (2y – 7)cm, 𝐶𝐷
̅̅̅̅ = (𝑥 + 7)𝑐𝑚 and 𝐴𝐷
̅̅̅̅ = (y+3)cm.
A. What is the value of x?
Solution:
𝐴𝐵
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ -------- Use parallelogram property 1
3x – 5 = x + 7
(3x -x) (– 5 + 5)= (x – x) (+ 7 + 5)
2x = 12
2𝑥
2
=
12
2
x = 6
B. What is the value of y?
Solution:
𝐴𝐷
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅ -------- Use parallelogram property 1
y + 3 = 2y – 7
y – 2y + 3 – 3 = 2y -2y – 7 – 3
-y = -10
y = 10
C. How long is ≅ 𝐴𝐷
̅̅̅̅?
𝐴𝐷
̅̅̅̅ = (y + 3)cm
𝐴𝐷
̅̅̅̅ = (10 + 3)𝑐𝑚
𝑨𝑫
̅̅̅̅ = 𝟏𝟑𝒄𝒎
3. Given a parallelogram below, Find the exact measure of the 4 angles?
Solution:
∠𝑻 + ∠ 𝒌 = 𝟏𝟖𝟎° ----- Use parallelogram property 3
(y + 40)º + 2(y + - 20)º = 𝟏𝟖𝟎°
C
A
D
B
(y + 40)º 2 (y - 20)º
K
A
T
S

12. 9
y + 40 + 2y – 40 = 𝟏𝟖𝟎°
3y = 𝟏𝟖𝟎
3𝑦
3
=
180
3
y = 𝟔𝟎°
∠𝑻 = (y + 40)°
∠𝑻 = (60 + 40)°
∠𝐓 = 𝟏𝟎𝟎°
∠𝐒 = 𝟏𝟎𝟎° ---- Using Parallelogram Property 2
∠𝑇 + ∠ 𝑘 = 180° ------- ----- Use parallelogram property 3
100° + ∠ 𝑘 = 180°
100° - 100° + ∠ 𝑘 = 180° − 100°
∠ 𝒌 = 𝟖𝟎°
∠ 𝑨 = 𝟖𝟎° ---- Using Parallelogram Property 2
III. Accompanying DepEd Textbook and Educational Sites
Mathematics 9 Learner’s Materials, First Edition, 2014, Merden L. Bryant,
Leonides E. Bulalayao, Melvin M. Callanta, Jerry D. Cruz, Richard F. De Vera,
Gilda T. Garcia, Sonia E. Javier, Roselle A. Lazaro, Bernadeth J. Mesterio, and
Rommel Hero A. Saladino
IV. Activity Proper
Directions / Instructions:
For further information about this lesson, please refer to Mathematics Learner’s
Material pages 314 - 319.
Exercises / Activities
Exercise 1:
DIRECTION: Refer to the given figure at the right and answer the following using the
different properties of parallelogram.
Given: MATH is a parallelogram.
1. 𝑀𝐴
̅̅̅̅̅ ≅_____
2. ∆MAH ≅ _____
3. 𝑀𝑆
̅̅̅̅ ≅ _____
4. ∆THM ≅ _____
5. ∠ATH ≅_____
6. If m∠MHT = 100°, then m∠MAT _____
7. If m∠AMH = 100°, then m∠MHT _____
8. If MH = 7, then AT = _____

13. 10
9. If AS = 3, then AH = _____
10.If MT = 9, then SM = _____
Exercise 2:
Directions: Using the figure at the right answer the following question.
1. Given HE = 2x
OR = x + 5
Find HE
2. Given: m ∠HER = 5y – 26
m ∠ROH = 2y + 13
Find: m ∠ROH
3. Given: m ∠OHE = 3 m ∠HER
Find: m ∠OHE and m ∠HER
4. Given: HZ = 4a – 5
RZ = 3a + 5
Find: HZ
5. Given: OZ = 12b + 1
ZE = 2b + 21
Find: ZE
4. Guide Questions
a. What is a parallelogram?
b. What can you say about the measures of the pairs of opposite sides and
angles of a parallelogram? How about its pair of consecutive angles?
c. What can you say about the diagonals of a parallelogram?
d. What are the different properties of parallelogram?
e. Do the properties of parallelogram be used in finding the measures of
each part of a parallelogram? How?
V. Reflection
Complete the statement.
I have learned that_______________________________________________
___________________________________________________________________.
I have realized that _____________________________________________
___________________________________________________________________.
I will apply _________________________________________________________________
_________________________________________________________________________________.

14. 11
V. Answer Key
Exercise
1:
1.
𝑇𝐻
̅̅̅̅
2.
ΔTHA
3.
𝑇𝑆
̅̅̅̅
4.
ΔMAT
5.
∠HMA
6.
100
7.
80°
8.
7
9.
6
10.
4.5
Exercise
2:
1.
10
2.
39°
3.
m
∠OHE
=
135°
;
m
∠
HER
=
45°
4.
35
5.
25