Math 9 Module
Math 9 Module
Math 9 Module
Quarter 3 - Module 4
Solving Problems Involving
Parallelograms, Trapezoids, and
Kites
Mathematics – Grade 9
Alternative Delivery Mode
Quarter 3 – Module 4: Solving Problems Involving Parallelograms, Trapezoids, and
Kites
First Edition, 2021
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Mathematics
Quarter 3 - Module 4
Solving Problems Involving
Parallelograms, Trapezoids, and
Kites
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, dear learners, can
continue your studies and learn while at home. Activities, questions, directions,
exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step
as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM.
This will tell you if you need to proceed on completing this module or if you need
to ask your facilitator or your teacher’s assistance for better understanding of the
lesson. At the end of each module, you need to answer the post-test to self-check
your learning. Answer keys are provided for each activity and test. We trust that
you will be honest in using these.
In addition to the material in the main text, notes to the Teachers are also
provided to our facilitators and parents for strategies and reminders on how they
can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of
this SLM. Use a separate sheet of paper in answering the exercise and tests.
Read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the
tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
This module provides varied activities that will help you learn about
quadrilaterals.
What I Know
Directions: Read each item carefully. Write the letter of your answer on a separate sheet
of
paper.
5. Which of the following quadrilaterals has diagonals that do not bisect each
other?
a. Trapezium b. Parallelogram c. Trapezoid d. Kite
8. The diagonals of a kite have lengths of 10cm and 9cm. What is the area of the
kite?
a. 19cm² b. 38cm² c. 45cm² d. 90cm²
9. Find the value of x in the parallelogram MILK.
M I
X + 40°
3x – 20° L
K
G I
110°
35°
E 35° V
a. 24 b. 30 c. 35 d. 50
1 2 3
4 5
7 8
9
1
0
DOWN
ACROSS
Fact or Bluff!
Directions: Identify if the given statement states a fact or a bluff by shading using your
crayon.
1.
2.
3.
4.
5.
A. Parallelogram is a quadrilateral with two pairs of opposite sides that are parallel.
W I
H S
m∠W = x + 15 Given
m∠W = 10 + 15 Substitute the value of x
m∠W = 25 solve for m∠W
T
R S
1. If OS
´ = 3x – 2, PT
´ = 2x + 10 and ER
´ = 14, how long is each base?
Substitute:
´
OS = 3x - 2 ´ = 2x + 10
PT Given
´ = 3(4) - 2
OS ´ =2(4) + 10
PT Substitute the value of x
´
OS=12−2 ´ = 8 + 10
PT Simplify
OS´ = 10 ´ =18
PT Final Answer
´ and ´¿ ≅ KE
Given: Quadrilateral LIKE is a kite with ĹI ≅ IK ´ .
L K
1. ´¿ is twice as long as ĹI . If the perimeter of the kite is 24cm, how long is ´¿?
P= LI
´ + IK ´ ¿´
´ + KE+ Formula
24 cm=x+ x +2 x+ 2 x Substitute all the given
24 cm=6 x Divide both sides by 6
4 cm=x Value of x
´ +
2. What is the area of the kite if one of the diagonals is 4 more that the other and IE
´ = 16in?
LK
´ (1st diagonal)
Let: x – length of IE
´ (2nd diagonal)
x + 4 – length of LK
´ + LK
IE ´ = 16 in Given
x + x+4 = 16 Substitution
2x + 4 = 16 Combine similar terms
2x = 16 – 4 Transposition
2x = 12 Divide both sides by 2
X=6 Value of x
´ =6
IE Substitute the value of x
´
LK = 6 + 4 = 10 Substitute the alue of x
1 Formula for the area of kite
A= (d d )
2 1 2
1 Substitution
A = (6)(10)
2
60 Solve for A
A=
2
A = 30 Area of Kite
What’s More
Independent Activity 1
Directions: Analyze the given questions. Choose your answers inside the box.
I
G
F
T
1. If IF
´ = 6cm, how long is ´¿ ? __________
2. If ǴI = 16cm, how long is TF´ ? _________
3-4 If ÓI = 6cm and OF ´ = 7cm, what is the length of IT ´ ?
´ ? ________ and GF
__________
5-6 If IT ´ = 18cm and OF
´ + GF ´ = 5cm, what is the length of IT
´ ?_________
´ ? _________
and the length of GF
A.
E M
4x – 40°
N x + 20° A
1. 4x – 40 + _____ = 180
2. 5x - _____ = 180
3. 5x = 180 + _____
4. 5x = _____
5. X = _____
E M
4x – 40°
B.
N x + 20° A
1. 4x-40 = _____
2.3 4x - _____ = 20 + _____
4. 3x = _____
5. x = _____
Independent Activity 2
Directions: Solve the following:
H G
I J
E F
1.
´ = 8 and
´ = x, HG
If IJ
´ = 12, what is the value of
EF
x?
4 10 20
2.
If IJ ´ = 14 and EF
´ = y + 3, HG ´
= 18, what is the value of y?
13 16 32
3.
´ = x, IJ=16∧¿
If HG ´
´ = 22, what is the value of
EF
x?
4 6 10
4.
´ = y-2, IJ
If HG ´ = 20 and
´ = 31, what is the value of
EF
y?
11 29 40
5.
6 10 14
Independent Assessment 2
Directions: Matching Type. Match column A with the correct answer in column B.
Use
the given isosceles trapezoid MEAN. Write the letter of your answer.
E
M
N A
Column A Column B
_____1. If m∠N = 2x-6 and m∠A = 82, what is x? A. 22
_____2. If m∠E = 2(y+4) and m∠M = 116, what is y? B. 26
_____3. If NE=56
´ ´ ?
, what is MA C. 44
_____4. If NE
´ = 2x+10 and ḾA = 4x-6, what is NE ´ ? D. 54
_____5. If ḾA = 3y + 7 and NE´ = 6y – 88, what is ḾA ? E. 56
Independent Activity 3
Show More What You Got!
Directions: Answer each problem carefully. Choose the corresponding letter from
the
kites given below.
F I S
10 L 24 E 97.5
15 42
_____1. The diagonals of a kite have lengths 6cm and 5cm. Find the area of the kite.
_____2. The diagonals of a kite have lengths 12cm and 7cm. Find the area of the
kite.
_____3. The diagonals of a kite have lengths 15cm and 13cm. Find the area of the
kite.
_____4. If the area of a kite is 96cm² and one of its diagonals is 8cm, what is the
length of the other diagonal?
_____5. The area of a kite is 180cm² and the length of the diagonal is 36cm. How
long is the other diagonal?
Independent Assessment 3
Directions: Solve for what is asked in each question.
d 1 = 14
d 2 = 21
6cm 6cm
10cm
d 1 = 11 cm
d 2 = 23 cm
A = 140cm²
d 1 = 28cm
d 2= ?
a. 4 b. 7 c. 15 d. 30
G I
110°
35°
E 35° V
2x – 50° L
K
H O
15. What is the measure of ∠2 in the parallelogram HOME? 105°
a. 75° b. 90° c. 105° d. 180°
E 2 M
Additional Activities
Direction: Solve the following problems
1. If the measure of one of the base angles of an isosceles trapezoid is 40°, what are
the measures of the other angles?
2. If the measure of one angle of an isosceles trapezoid is x° and the angle opposite it
is (x + 20) °, what is the measure of the angle?
´ = 2x + 3 and EC
3. In Parallelogram ONCE, if ON ´ = 4x-5, find ON
´ and CE
´ .
Answer Key