Mathematics 4 Quarter 3 Module 3: Triangles and Quadrilaterals

CO_Q3_Mathematics 4_ Module 3

Mathematics

Quarter 3 – Module 3: Triangles and Quadrilaterals

[illustration: group of learners reading and studying outdoors and at a desk, with a globe and a lantern]

Mathematics – Grade 4 Alternative Delivery Mode Quarter 3 – Module 3: Triangles and Quadrilaterals First Edition, 2020

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Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio

Printed in the Philippines by ____________________________________

Department of Education – Region V

Office Address: Regional Center Site, Rawis, Legazpi City 4500 Telefax: 0917-178-1288 E-mail Address: region5@deped.gov.ph

Development Team of the Module

Writers: Elena D. Hubilla Editors: Loyd H. Botor Reviewers: Loyd H. Botor Illustrator: Jason C. Borabo Layout Artist: Emmanuel S. Gimena Jr. Management Team: Gilbert T. Sadsad, Francisco B. Bulalacao Jr., Grace U. Rabelas, Ma Leilani R. Lorico, Monserat D. Guemo, Florena M. Deuna

4

Mathematics

Quarter 3 – Module 3: Triangles and Quadrilaterals

Introductory Message

This Self-Learning Module (SLM) is prepared so that you, our 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 Teacher 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 exercises and tests. And 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.

[illustration: target with arrow]

What I Need to Know

This module was designed in order to assist you to learn the different kinds of triangles and quadrilaterals.

In this lesson, you will learn about the different kinds of triangles according to sides and angles and identify and describe the different kinds of quadrilaterals: square, rectangle, parallelogram, trapezoid, and rhombus. You will also describe the different attributes/properties of triangles using concrete objects/models. The learning activities will allow you to explore, discover and appreciate the different kinds of triangles that can be seen in different objects around us. You will also be taught on how to describe and illustrate the different kinds of triangles in the succeeding activities.

After going through this module, you are expected to:

1. describe the attributes/properties of triangles and quadrilaterals using concrete objects or models;
2. identify and describe triangles according to sides and to angles; and
3. identify and describe the different kinds of special quadrilaterals: square, rectangle, parallelogram, trapezoid, and rhombus.

[illustration: pencil]

What I Know

Group the figures below into triangles and quadrilaterals by writing the figure number in the correct column of the table. Write your answer on a separate sheet of paper.

[illustration: ten numbered plane figures in a rounded box. Figure numbers as printed: 1 (thin slanted triangle), 2 (rhombus), 3 (trapezoid), 4 (right triangle), 5 (triangle), 6 (shaded right triangle), 7 (rectangle), 8 (parallelogram), 9 (triangle outline), 10 (square)]

Triangles	Quadrilaterals

Go to the Answer Key to check your answers.

[illustration: smiling boy]

CONGRATULATIONS! If you got a score of 9 or 10, you should not have any difficulty studying the lesson in this module. If you got a score of 8 or below, you may need to study the lesson more carefully and do all the given activities.

Lesson 1: Attributes of Triangles and Quadrilaterals

What’s In

[illustration: black-and-white pattern of overlapping irregular triangles] [illustration: black-and-white pattern of interlocking quadrilaterals]

https://wallhere.com/en/wallpaper/852616 https://www.dreamstime.com/illustration/quadrilaterals.html

Do you like patterns? Look at the patterns above. Which one do you prefer? What shapes do you see in the first pattern? What about in the second? How many sides and corners does each shape in the first pattern have? What about in the second?

What’s New

[illustration: two black-and-white T-shirts, one with a triangle pattern and one with a checkered pattern]

https://www.zazzle.com/black_and_white_checkered_patterns_stylish_elegant_all_over_print_t_shirt-256805711310915313

Twin brothers Larry and Garry bought shirts out of their savings. Although they were twins, they have their own favorite designs. Larry bought the one on the left while Garry bought the one on the right. What do you think is Larry’s

[transcriber’s note: the text in this box ends at “Larry’s” on this page; the remainder of the question is not visible here]

[illustration: magnifying glass with question mark]

What is It

The shirt Larry bought shows a pattern consisting of 3-sided polygons. These 3-sided polygons are called triangles. Triangles also have three corner points.

Below are some examples of triangles with different sizes and shapes.

[illustration: six triangles of different sizes and shapes]

The pattern in the shirt Garry bought shows four-sided polygons. Four-sided polygons are called quadrilaterals. Quadrilaterals also have four corners. There are different kinds of quadrilaterals. Here are some more examples.

[illustration: eight quadrilaterals of different shapes, including a parallelogram, a kite-like quadrilateral, a trapezoid, a square, a rhombus, a rectangle, an irregular quadrilateral, and a trapezoid]

Lesson 2: Kinds of Triangles

What’s In

Let us recall the properties of triangles and quadrilaterals.

Triangles are polygons with three sides and three corners. Their sides may be of equal or of different lengths.

Quadrilaterals are polygons with four sides and four corners. There are different kinds of quadrilaterals. Some quadrilaterals have two or more equal sides. Also, some quadrilaterals have one or two pairs of parallel sides.

What’s New

[illustration: a house with a triangular roof, a large arrow pointing toward the roof’s left slope, two square windows with X marks, and a central window with a grid of panes]

Let us look at the top part of the house above. How many sides does it have? What is its shape? Yes, it has three sides and is in the shape of a triangle.

Let us look at the windows this time. How many triangles in all do you see in the two windows?

Do you know how triangles are classified? Today, we will learn about how triangles are classified. We will also learn about the different kinds of triangles.

KINDS OF TRIANGLES ACCORDING TO SIDES

Equilateral triangle – a triangle which has three equal sides

[illustration: equilateral triangle with tick marks on all three sides] 5 cm 5 cm 5 cm

Isosceles triangle – a triangle which has two equal sides

[illustration: isosceles triangle with tick marks on two sides] 7 cm 7 cm 5 cm

Scalene triangle – a triangle which has no equal sides

[illustration: scalene triangle with no tick marks] 6 cm 9 cm 10 cm

KINDS OF TRIANGLES ACCORDING TO ANGLES

Right triangle – a triangle which has a right or 90˚- angle

[illustration: right triangle with a square right-angle mark at the lower left corner]

Acute triangle – a triangle which has three acute angles or angles measuring less than 90˚

[illustration: acute triangle with angles labeled] 60⁰ 70⁰ 50⁰

Obtuse triangle – a triangle which has one obtuse angle or an angle measuring greater than 90˚

[illustration: obtuse triangle with angles labeled] 50° 100° 30°

Equiangular triangle – a triangle which has three equal angles each measuring 60˚.

[illustration: equiangular triangle with angles labeled] 60⁰ 60⁰ 60⁰

What is It

Let us try to have a clearer understanding of how triangles are classified as we get to know the different kinds of triangles.

KINDS OF TRIANGLES ACCORDING TO SIDES

Triangles may be classified according to their sides. The kinds of triangles according to their sides are the equilateral, isosceles and scalene triangles.

Equilateral triangles

An equilateral triangle is a triangle with three equal sides.

The triangles below are all equilateral triangles. They have three equal sides.

[illustration: three equilateral triangles with tick marks on their sides, showing equal sides]

The symbols “I”, or “II”, etc. are used to mark parts of figures. When parts of the same or of different figures are marked using the same symbols, that means those parts have equal measures or are congruent.

Isosceles triangles

An isosceles triangle is a triangle with two equal sides.

The triangles below are isosceles triangles**.** They have two equal sides.

[illustration: three isosceles triangles with tick marks on two sides of each]

Scalene triangles.

A scalene triangle is a triangle with no equal sides.

The triangles below are scalene triangles**.** They have no equal sides.

[illustration: three scalene triangles, none with equal sides]

KINDS OF TRIANGLES ACCORDING TO ANGLES

Triangles may also be classified according to their angles. The kinds of triangles according to their angles are the right triangle, the obtuse triangle and the equiangular triangle.

Right triangle

A right triangle is a triangle with a right angle or an angle which measures 90˚.

The triangles below are all right triangles**.** They all have a right angle.

[illustration: three right triangles, each with a right angle marked; labels: 90˚, 90˚, 90˚]

Acute triangles

An acute triangle is a triangle with three acute angles or angles each measuring less than 90˚.

The triangles below are all acute triangles. All their angles are acute or measure less than 90˚.

[illustration: three acute triangles; the middle one labeled 70˚, 50˚, 60˚; the other two have angle marks only]

Obtuse triangles

An obtuse triangle is a triangle with an obtuse angle or an angle which measures greater than 90˚.

The triangles below are all obtuse triangles. They all have one obtuse angle or an angle which measures greater than 90˚.

[illustration: two obtuse triangles; first labeled 130˚, 25˚, 25˚; second labeled 40˚, 30˚, 110˚]

Equiangular triangles

An equiangular triangle is a triangle with three equal angles each measuring 60˚. An equiangular triangle is actually a special kind of an acute triangle.

The triangles below are all equiangular triangles**.** All their angles are equal and each measure 60˚.

[illustration: three equiangular triangles, each angle labeled 60˚]

It is important to know that all equilateral triangles are equiangular triangles.

NOTE: The total measure of the three angles of a triangle is equal to 180˚.

What’s More

Activity 1. “Match Me Up”

Match the figure with the correct description. Write the letter of the correct answer on the blank provided. Write your answer on a separate sheet of paper.

A	B
_____1. scalene triangle	a. all its angles measure less than 90˚
_____2. isosceles triangle	b. all its three sides are equal
_____3. equilateral triangle	c. it has no equal sides
_____4. acute triangle	d. all its three angles are equal and measure 60˚
_____5. equiangular triangle	e. it has two equal sides
	f. exactly two angles are 60˚

Activity 2. “Name It”

Fill in the blanks with the kind of triangle described given the measurements of its angles below. Write your answer on a separate sheet of paper.

1. m∠A = 125˚, m∠B = 30˚, m∠C = 25˚ _______________
2. m∠A = 60˚, m∠B = 60˚, m∠C = 60˚ _______________
3. m∠A = 90˚, m∠B = 45˚, m∠C = 45˚ _______________
4. m∠A = 110˚, m∠B = 40˚, m∠C = 30˚ _______________
5. m∠A = 48˚, m∠B = 57˚, m∠C = 75˚ _______________

Activity 3. “Right Me”

List all the letters that are inside right triangles. Write your answer on a separate sheet of paper.

[illustration: grid with ten triangles labeled A, B, C, D, E, F, G, H, I, J]

Check your answers with the Answer Key of the module. A score of 13 -15? GREAT! You understood the lesson well. Got a score of 10 – 12? Study carefully the lesson and the activities given. A score below 10? You may need somebody to assist you.

What I Have Learned

Let us recall. There are different kinds of triangles. They are classified according to the lengths of their sides and also according to the measures of their angles.

KINDS OF TRIANGLES ACCORDING TO SIDES

Equilateral – all three sides are equal Isosceles – two sides are equal Scalene – no sides are equal

KINDS OF TRIANGLES ACCORDING TO ANGLES

Right triangle – one angle is right or has a measure of 90˚ Acute triangle – all angles are acute or have measures less than 90˚ Obtuse triangle – one angle is obtuse or has a measure greater than 90˚ Equiangular triangle – all three angles are equal or have measures of 60˚.

All equilateral triangles are also equiangular.

What I Can Do

Using different kinds of triangles, draw a kite or a toy that you would want to play with. Write your answer on a separate sheet of paper.

Assessment

I. Fill in the blanks with the correct word from the box below. Write your answer on a separate sheet of paper.

isosceles | equilateral | right | obtuse equiangular | acute | corners | scalene triangle | three angles | quadrilateral

_____ 1. I am a triangle with three 60˚ angles. _____ 2. I have two equal sides. _____ 3. One of my angles measures 90˚. _____ 4. I have no equal sides. _____ 5. I am a triangle with an angle greater than 90˚. _____ 6. All my angles are less than 90˚. _____ 7. All my three sides are equal. _____ 8. A triangle is a polygon with ______ sides and _____ 9. three ______. _____ 10. I am a three-sided polygon.

Additional Activities

Who am I? Identify the kind of triangle and draw an example of each. Write your answer on a separate sheet of paper.

1. I am a triangle with no sides equal.
2. I am a triangle with 3 equal sides.
3. I am a triangle with an obtuse angle.
4. I am a triangle with 2 equal sides.
5. I am a triangle with a 90˚ angle.

What I Know

You need a sheet of paper for the activities.

I. Which word inside the box gives the name of the figures below? Write your answers on your answer sheet.

[illustration: five plane figures numbered 1 to 5: 1. rectangle, 2. trapezoid, 3. rhombus, 4. parallelogram, 5. square]

rhombus | kite | rectangle | parallelogram | square | trapezoid

II. Which of the figures below are quadrilaterals? Copy the quadrilaterals on your answer sheet.

[illustration: eight plane figures in a row: a triangle, a parallelogram, a square, an irregular octagon-like figure, a pentagon, a rhombus, a rectangle, and a trapezoid]

Refer to the Answer Key to check your answers.

You’re EXCELLENT if you got a score of 8 -10. You already have a clear understanding of the lesson in this module. If your score is 7 or below, kindly study carefully the lesson and the activities.

Lesson 3 Kinds of Quadrilaterals

What’s In

Hello kids. Do you recall your lesson on triangles? How do we classify triangles? What are the different kinds of triangles? How do they differ from one another?

Match the items in column A with the correct descriptions in column B. Write the letter of the correct answer. Write your answer on a separate sheet of paper.

A	B
____ 1. Equilateral triangle	a. All its angles are less than 90˚
____ 2. Acute triangle	b. All its three sides are equal
____ 3. Scalene triangle	c. It has no equal sides
____ 4. Isosceles triangle	d. All its three angles measure 60˚
____ 5. Equiangular triangle	e. It has two equal sides

Check your answers with the Answer Key. If you got a score of 5, then you are ready to study this module. If not, you need to study the lesson on triangles.

What’s New

The prices of basic commodities are continuously increasing. Even prices of vegetables are going up. Knowing that they have to eat vegetables to keep their family healthy, Mr. and Mrs. Manalig decided to have a vegetable garden in their backyard.

With their own backyard vegetable garden, the Manalig family will not only stay healthy, they will also be saving money. They can also be very sure that the vegetables they would be eating are free of harmful chemicals as they also plan to go for organic gardening.

[photo: celery growing in a rectangular container] [photo: saluyot growing in a wooden frame garden bed] [photo: eggplant plants growing in a wooden frame garden bed] [photo: seedlings in a seed tray and lettuce growing in a foam box]

What vegetables does the Manalig family have in their garden. They have celery, saluyot, eggplant seedlings, pepper and lettuce. Do you also eat vegetables? Do you think it is good to have our own vegetable garden at home?

Let us look at the containers the Manaligs used in their garden. Observe the shape of the containers.

What is It

All the containers used in the garden of the Manalig Family are rectangles in shape. They all have four sides and four corners. These shapes are also called quadrilaterals.

All four-sided figures or polygons are called quadrilaterals. Some of them have two or more equal sides. Quadrilaterals may also have one or two pairs of parallel sides.

Although all quadrilaterals have four sides, we can see that they vary in sizes and shapes. Let us now look at the different kinds of special quadrilaterals.

KINDS OF QUADRILATERALS

[illustration: square] This is a square. It has four equal sides and opposite sides are parallel. All its four corners are right angles or measure 90˚.

[illustration: rectangle] This is a rectangle. Opposite sides are equal and parallel. All its four corners are right angles or measure 90˚.

[illustration: parallelogram] This is a parallelogram. Opposite sides are equal and parallel. Angles at opposite corners have the same measurements.

[illustration: trapezoid] This is a trapezoid. It has one pair of parallel sides.

[illustration: rhombus] This is a rhombus. Its four sides are equal. Opposite sides are parallel and opposite angles are equal.

All four-sided figures are Quadrilaterals. They are classified according to the lengths of their sides and the measures of their angles.

Let us have a clearer understanding of the kinds of quadrilaterals.

Figure	Name	Description/Properties
[illustration: square]	Square	All sides are equal. Opposite sides are parallel. All of the four corners are right angles.
[illustration: rectangle]	Rectangle	Opposite sides are equal and parallel. All four corners are right angles.
[illustration: parallelogram]	Parallelogram	Opposite sides are equal and parallel. Opposite corners have the same measure.
[illustration: trapezoid]	Trapezoid	Has one pair of parallel sides.
[illustration: rhombus]	Rhombus	All sides are equal. Opposite sides are parallel. Opposite angles are equal.

[illustration: speech bubble from a girl character] I hope you now understand what a quadrilateral is and know its different types.

What’s More

Activity 1. “Match Us Up”

Match the quadrilateral with the object having its shape. Write your answer on a separate sheet of paper.

A	B
___ 1. square	A. [photo: textured mesh object]
___ 2. rhombus	B. [illustration: lamp shade shaped like a trapezoid]
___ 3. rectangle	C. [illustration: diamond-shaped object split by a line]
___ 4. parallelogram	D. [photo: dark rectangular object]
___ 5. trapezoid	E. [illustration: parallelogram-shaped textured sheet]

Activity 2. “Find Me”

Identify the quadrilaterals and copy them on your answer sheet.

[illustration: a box containing 18 outlined shapes of varied kinds, including quadrilaterals such as squares, rectangles, trapezoids, parallelograms, rhombuses, and non-quadrilateral shapes such as triangles, a hexagon, and irregular curves]

What’s More

Activity 3.

Group the objects according to their shapes. Copy them in the correct quadrilaterals. Write your answer on a separate sheet of paper.

Square	Rectangle	Rhombus	Parallelogram	Trapezoid

[illustration: a row of nine outlined quadrilaterals of different shapes and sizes, to be grouped]

What I Have Learned

Let us remember the following:

Four-sided polygons or figures are called Quadrilaterals. There are different kinds of quadrilaterals. Some quadrilaterals have special properties and have been given special names. These are the square, the rectangle, the parallelogram, the trapezoid and the rhombus.

Figure	Description
[illustration: square]	A square has four equal sides and opposite sides are parallel. All four corners are right angles or measure 90º.
[illustration: rectangle]	A rectangle has two pairs of equal and parallel sides. All its four corners are right angles ore measure 90º.
[illustration: parallelogram]	A parallelogram has two pairs of equal and parallel sides. Angles at opposite corners have the same measurements.
[illustration: trapezoid]	A trapezoid has one pair of parallel sides.
[illustration: rhombus]	A rhombus has four equal sides. Its opposite sides are parallel and opposite angles are equal.

What I Can Do

Using the different kinds of quadrilaterals, design your own backyard vegetable garden. Write your answer on a separate sheet of paper.

Assessment

I. Select the correct answer from the box. Write your answer on a separate sheet of paper.

rhombus rectangle parallelogram square trapezoid

1. I have two pairs of equal and parallel sides. The angles at my opposite corners have the same measure. What am I?
2. I have four equal sides. All my four angles measure 90˚. What am I?
3. I have only one pair of parallel sides. What am I?
4. I have two pairs of equal and parallel sides. All of my corner measure 90˚.
5. I have four equal sides. My opposite sides are parallel, my opposite angles are equal.

II. Draw objects showing the different kinds of quadrilaterals. Write your answer on a separate sheet of paper.

1. square
2. rectangle
3. parallelogram
4. rhombus
5. trapezoid

Additional Activities

Draw a toy using a combination of the different quadrilaterals. Write your answer on a separate sheet of paper.

[illustration: five quadrilateral shapes labeled rhombus, rectangle, parallelogram, square, trapezoid]

Answer Key

[transcriber’s note: this page is printed rotated 180 degrees; the text below is transcribed in its upright reading.]

LESSON 1

What I Know

[illustration: a sorting diagram of geometric shapes, with the label “Triangles” under the group of triangles and the label “Quadrilaterals” under the group of quadrilaterals]

What’s More

Activity 1

[illustration: a triangle-shaped sorting diagram containing the numbers 15, 17, 18, 22, 23, 24, 25, above a box containing the numbers 1 to 10]

Activity 2

Answers may vary.

Assessment

1. Triangles are polygons with three sides and three corners.
2. Quadrilaterals are polygons with four sides and four corners.

What I Can Do

[illustration: four shapes of quadrilaterals arranged side by side]

Additional Activities

Answers may vary.

LESSON 2

What I Know

1. right
2. acute
3. obtuse
4. equiangular
5. isosceles
6. scalene
7. equilateral
8. triangle
   9.-10 angles, sides

What’s More

Activity 1

1. c
2. e
3. b
4. a
5. d

Activity 2

1. obtuse
2. equiangular
3. right
4. obtuse
5. acute

Activity 3

C, G, F, H, I

Assessment

1. equiangular
2. isosceles
3. right
4. scalene
5. obtuse
6. acute
7. equilateral
8. three
9. corners
10. triangle

What I Can Do

Answers may vary.

Additional Activities

1. scalene triangle
2. equilateral triangle
3. obtuse triangle
4. isosceles triangle
5. right triangle

[illustration: five triangles matching the numbered items above]

What’s In

1. b
2. a
3. c
4. e
5. d

What’s More

Activity 1

1. d
2. c
3. a
4. e
5. b

Activity 2

[illustration: eight plane figures in a scattered arrangement: trapezoid, rectangle, parallelogram, rhombus, square, and rectangle shapes]

What I Can Do

Answers may vary.

What’s More

Activity 3

Square	Rectangle	Rhombus
[illustration: square and a smaller square]	[illustration: rectangle]	[illustration: rhombus]
[illustration: parallelogram]		[illustration: trapezoid]

[transcriber’s note: the parallelogram cell spans the first two columns of the printed table]

Additional Activities

Answers may vary.

Assessment

I.

1. Parallelogram
2. Square
3. Trapezoid
4. Rectangle
5. Rhombus

II.

Answers may vary.

LESSON 3

What I Know

I.

1. rectangle
2. trapezoid
3. rhombus
4. parallelogram
5. square

II.

[illustration: row of five plane figures: parallelogram, square, rhombus, rectangle, and trapezoid]

References

DepEd Order No. 12, s. 2020. Adoption of the Basic Education Learning Continuity Plan for SY 2020-2021 In Light of the Covid-19 Public Health Emergency. June 19, 2020. p. 342.

dreamstime.com. 2021. Quadrilaterals Illustrations & Vectors. [online] Available at: <https://www.dreamstime.com/illustration/quadrilaterals.html> [Accessed 23 March 2021].

Guadarrama, MT.A., Butaran, A.C., De la Cruz, L., Rieta, T.A. & Zotomayor, P.A. (2015). Number Smart (Worktext in Mathematics). Rex Book Store.

Nctm.org. 2021. Sorting Polygons – National Council of Teachers of Mathematics. [online] Available at: <https://www.nctm.org/ClassroomResources/Illuminations/Lessons/Sorting-Polygons/> [Accessed 23 March 2021].

Wallhere.com. 2021. [online] Available at: <https://wallhere.com/en/wallpaper/852616> [Accessed 23 March 2021].

zazzle.com. 2021. [online] Available at: <https://www.zazzle.com/black_and_white_checkered_patterns_stylish_elegant_all_over_print_t_shirt-256805711310915313> [Accessed 23 March 2021].

For inquiries or feedback, please write or call:

Department of Education – Bureau of Learning Resources (DepEd-BLR)

Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600

Telefax: (632) 8634-1072; 8634-1054; 8631-4985

Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph