GEOMETRIC SHAPES AND 3D SHAPES USED IN MATHEMATICS 4 .PDF

A LESSON IN MATH 4

1. le Shapes

Geome

Equivalency Learning Material

Philippines Nonformal Education Project
(ADB-Assisted)

Bureau of Nonformal Education
DEPARTMENT OF EDUCATION,
CULTURE AND SPORTS

2. 1 eu cenimeters (em) = 000 cu millimeters (mm?) qua (0,

eu meins) 1.000000 em \

on zu)

2 pins au
Aqua (a)

° a Imperial
iron Length Long
milimeer (ny 2 10 mise (um) oot cy min a
À comimetertem) 2 10 meer (rm) yards) 3 fe)
1 occ (dim) = 10 cemimetrs (em) Emite 1760 yards 90)
1 meter (m) 10 deceo (em) = 106m 5280100
1 decametr (dam) = LO mein (m) 1 mais mie 20254 yuds Od)
hscometer hm) = VO desmeter (dam) {80 fest)
tometer m) 10m = 1.000 meters (m)
A, ue
ase Tome @ Sa
Tecna TOO migas mg) pour ib) = 160unces 2)
1 gras (ig) 1000 gra €) 1 tone 1 pods (Ib)
Lome 1000 logs (6) Y hundrod weight (en) = 112 pounds (1)
ary Den
Volume,
Tim ZEN Im) sore
Y solis (kD 1.000 Hees) Tomo 0d en

Area

Fa cotes (em) = 1000 5 mince (m)
aq meters (m)

ee (a)
se Kama ho)

10000 Sg emimeier (em) guaro yard 0)
10000 sa metes (m) Lace
= 100 hectares (a) 1 sg mie

Tr sg noes
Sq tect’)

D yards)
aces

Time

Y minuto = 60seconds >

hour = 60 minutes

aay = 2 hows

Luck = 70

1 mon = 4 weeks (approx) x 12

I year = FE months = 365 days «a

366 days in leap yea

‘decode = 10 yes 212 4

Yes = 100 years = 10 decades aise

Y millennium = 1.000 yess = 10 cents
ed bee 8

Math Symbols s|s w

+ pls (addition) sise

= mines (ubracton) ale à

% mes (lle)

À divided by (vision) ss te
equal sign als: ıs

= noregalı

equivalen sign wo] 10 20

3 gresterthin ale

2 destin

2 ercserthanoreguatto wale e

© — tessthen ur ogul to

= plusormines

Multiplication Table

É

6

a
RAB

38
ss
Es

835

3. Geometric Shapes

Copyright 2001
Bureau of Nonformal Education
DEPARTMENT OF EDUCATION,
CULTURE AND SPORTS

All rights reserved. No part ofthis module may be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or by any information storage
and retrieval system, without the prior written permission from the publisher.

Published in the Philip

by:

Bureau of Nonformal Education
Department of Education, Culture and Sports
S/F Mabini Bldg, DECS Complex
Meralco Avenue, Pasig City, Philippines
‘Tel. No. (02) 635 - $189 Fax No: (02) 635 - 191

4. ReruRuI or rie
DEPARTMENT OF EDUCATION,
DECS Campe, Meco Aue

ass, mie

My dear NFE A&E Learners,

Welcome to the Nonformal Education Accreditation
and Equivalency (NFE A&E) Learning Program of the
Department of Education, Culture and Sports (DECS). NFE
‘A&E is a new nonformal approach to learning which
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‘The program is built around a uniquely nonformal
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prepared leaming modules at two learning levels (elementary
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‘The modules will also prepare you to take an NFE A&E Test at
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We hope you find the modules interesting, useful and challenging,
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however, are skills which are essential for you to progress in an ever-
‘changing and increasingly competitive Filipino and global society. |

Good luck and mabuhay!

Roux € Rove
RAUL S, ROCO
Seay

6. QB what Is This Module About?

In our daily lives, we do not notice that we are dealing with geometric
shapes. How do you describe the shape of your notebook? I it similar o the
shape ofthis module? What isthe shape of your house? How many sides
(does ithave? These are only some of the questions that this module will

What Will You Learn From This Module?

‘After studying this module, you should be able to:

+ identify the different kinds oflines;

‘+ explain the concept of congruence;

+ define what rays, angles, plane figures and space figures are; and

+ identify the different kinds of angles, plane figures and space figures.

& Let's See What You Already Know

Before you start studying this module, take this simple test first to find out
how much you already know about the topics to be discussed.

A. Write Tin the blank ifthe statement is true and F ifit is false,
1. A sphere has no base.

2. Twoline segments are congruent if they have the same
measurement

3. A polygon with four equal sides is called a rectangle.
4. All prisms are cubes.

5. Aline has no beginning and no end.

7. B. Encirclethe letter ofthe correct answer to each of the following.

1. A has two circular bases.
a cone ©. cylinder
D. circle d. sphere

2. A ___ has three sides and three comers.
a triangle ©. rectangle
b. square d. trapezoid

3. A ___ has four equal sides and four comers.
a. rectangle ©. trapezoid
b. square d. thombus

4, Three-dimensional shapes are called

a. triangles ©. space figures
b. cones d. planes
5. Two line segments are __iftheir measurements are the same.
a. equivalent ©. similar
b. congruent d. adjacent

Well, how was it? Do you think you fared well? Compare your answers,
with those in the Answer Key on page 28 to find out

Fall your answers are correct, very good! This shows that you already
know much about the topics in this module. You may stil study the module to
review what you already know. Who knows, you might a learn a few more new
things as well

‘If you got a low score, don’t feel bad. This means that this module is for
you. It will help you understand some important concepts that you can apply
in your daily life, you study this module carefully, you will lear the answers
o al the items in the test and a lot more! Are you ready?

You may go now to the next page to begin Lesson 1.

8. Lesson 1

Lines and Angles

After studying this lesson, you should be able to:

+ define whata line is;
+ explain the concept of congruence;
+ define what rays and angles are; and

+ identify the different kinds of angles.

Pe Let's Try TI

Look at the drawings below. Then identify them according to the kinds of
lines they are. Refer to the list following the drawings.

A +

9. E. } a‘
1. straightlines

a. parallellines
b.. intersecting lines
©. perpendicular lines

2. curved ines

Compare your answers with mine below.

1. The ines in letters A to D are all straight ines. The lines in Bare
parallel, those in Care intersecting and those in D are perpendicular,

2. The lines in letter E are curved lines,
How well did you do? Were your answers similar to mine? Ifthey were,
that’s very good. You already know how to identify the different kinds of

lines, If they were not, just pay attention to this lesson and you will know a
whole lot about lines.

a Let's Learn

Are you familiar with the lines and their kinds now? Were you able to
identify the lines in the drawing as to their kinds?

10. Aline has no definite beginning and end. I can only be measured when
wo points called endpoints are set on either side of it. These points represent
the beginning and the end of the given lin, which is then more properly called
a line segment.

From the previous activity, you can see that there are basically two kinds
of lines—straight and curved lines,

lex Tr

‘Straight lines are further subdivided into the following kinds:

1. Parallel lines are lines on the same plane which run beside each
other without meeting at any point no matter how far they are
extended.

—_
oo

2. Intersecting lines, on the other hand, are lines on the same plane that
intersect with each other at least at one point.

3. Perpendicular lines are lines on the same plane that intersect each
other at one point and form 90*-angles,

11. & Let's Review

Determine whether each of the sets oflines are parallel, intersecting or
perpendicular. Write Pa for parallel, I for intersecting and Pe for perpendicular
in the spaces provided before the numbers.

e
2
yA

‘Compare your answers with those in the Answer Key on page 28. Did you
getall the answers right?

12. & Let’s Think About This

Do you know what the word congruence means? It refers to the state of
agreeing or coinciding. What does this mean? Read on to find out.

$5 Let's Study and Analyze

Look at the line segments in the drawing below. Try measuring them with a
ruler, Are they equal in length?

A B

E D

Yes, they are! We can therefore say that Line Segment AB or AB (read as
“Line Segment AB”) is congruent to CD.

Look at a clock. Do you know where its hands are? What do they remind
you of?

ik About This

‘The hands of a clock are examples of rays, lines that have a beginning but
no definite end. They can go on and on in one direction. They form an angle
‘when they meet ata certain point as in the hands on the face of a clock.

Do you know what kind of angle the hands of the clock above show?

13. If you answered that they form an obtuse angle, then you are right. Ifyou
were not able to answer correctly read on to find out more about angles and
their different kinds.

What is an angle anyway? An angle isthe figure formed when two rays or
lines intersect at one point. Its kinds include:

1. Acute angle—This is an angle that measures less than 90",

2. Right angle—This is an angle that measures exactly 90°.

!
|

LE

3. Obtuse angle This is an angle that measures more than 90° but less.
than 180°

4. Straight angle— This is an angle that measures exactly 180°.

+>

14. Py Let's Try This

Look at the drawing below. Identify what kinds of angles those mentioned

A
A
A
: e
|
i de
—> o
— 3 ano
x eee
— «ms

Compare your answers with those in the Answer Key on page 28. Did you
getall the answers right?

15. 2 Let's See What You Have Learned

Match the items in Colurmn A with those in Column B.

Column A
1. A figure that has no definite a
beginning and end <
2, Twolines that do not and will not
intersect no mater how far they are a
extended ä
3. ‘Tvolines that forma 90°-angle ae
_— 4. Two lines hat cross each other E
at any one point
5, Refers tothe state of agreeing or de
coinciding »

6. A figure that has a beginning but no i
definite end

7. Anangle which measures less than
90°

8. Anangle which measures exactly 90°

9, Anangle which measures more
than 90° but less than 180°

10. Anangle which measures exactly
180°

Column B

Perpendicular
Ray

Obiuse
Parallel
Congruence
Right
Intersecting
Acute
Straight

Line

Compare your answers with those in the Answer Key on page 29. Did you
get all the answers right? If you did, that's very good. You may then proceed
to the next lesson. If you did not, that’s okay. Just review the parts of the

lesson you didn't understand very well before going to Lesson 2.

16. 8 Let's Remember

.

“Aline has no definite beginning and end.
The two basic types of lines are straight and curved lines.

There are three kinds of straight lines —paralle, intersecting and

perpendicular ines.
‘The term congruence refers 10 the state of agreeing or coinciding,

‘The four basic kinds of angles are acute, right, obtuse and straight
angles.

17. Lesson 2

Plane Figures

‘After studying this lesson, you should be able to:
+ identify the different kinds of plane figures;
+ differentiate one kind of plane figure from another; and

+ determine whether two given plane figures are congruent or not,

& Let’s Think About This

Look at the drawing below. Are you familiar with the different kinds of
plane figures? What plane figures do you see in the given drawing? List their
names down in the spaces provided.

18. 10.

Compare your answers with those in the Answer Key on page 29. Did you
getall the answers right?

a Let's Learn

‘There are many kinds of plane figures but we will only focus on the
following in our discussion.

1. Trapezoid—A quadrilateral having only two parallel sides,

2. Parallelogram—A quadrilateral with opposite sides parallel and
equal

3. Rhombus—A parallelogram with four equal sides and no right
angles.

5

19. 4. Rectangle—A parallelogramall of whose angles are right angles.

5. Square—A rectangle with all four sides equal.

6. Polygons —Closed plane figures bounded by straight lines.

a. Teiangle—A polygon having three sides.

b. Pentagon—A polygon having five sides.

20. ©. Hexagon-—A polygon having six sides.

ne,

4. Octagon—A polygon having eight sides.

®

7. Circle—A closed plane curve every point of which is of the same
distance froma fixed point within the curve.

O

8. Oblong—A plane deviating from a square, circular or spherical form
byelongationin one dimension.

QS

21. > Let's Try This

Make your own drawing similar tothe one on page 12 using all he shapes
‘you just leamed about. Use the space provided below for your drawing.

Have your Instructional Manager check your drawing. Ask him/her for
some feedback before going o the next part of the lesson,

22. 2 Let's See What You Have Learned

Match the names of shapes in Column A with the corresponding figures in
Column B. Write the letters of the correct answers in the spaces provided
before the numbers.

— i en
__. 2. Parallelogram b. ZN

_ 3 Rhombus N
HE xy
_ uf oe
Be .

à ge 2 OY
== \
—— 7. Pentagon \ 7
—— 8 Hexagon hy

9. Circle i CN

. 10, Oblong CO
Su

23. Compare your answers with those in the Answer Key on page 30. Did you
get all the answers right? If you did, that’s very good. You may then go to the
next lesson. If you didn't, just review the parts of the lesson you didn't
understand very well before going to Lesson 3.

a Let's Remember
+ Themost common plane figures include the following:
1. trapezoid;
parallelogram;
3. hombus;
4. rectangle;
5. square;
6. triangle,
7. pentagon;
8. hexagon;
9. octagon;
10. cele; and
11, oblong,

24. Lesson 3

Space Figures

After studying this lesson, you should be able to:
© define what space figurés are; and
+ identify the different kinds of space figures.

e Let's Think About This

Look at he following common household items. What space figures do
they remind you of?

Fire, et us nti what the items in the picture above are. In the picture
an be seth & Ptcher, a box, an ice cream cone and a basketball. The pitcher
is an exdinple of a cylirider. The box is an example ofa cube. The ice cream
cone is an example of a cote, Finally, the basketball is an example ofa sphere.

Did: i ihe answers right? Why don’t you read on to find out more
about py

19

25. a Let's Learn

Space or three-diniensional figures are ones that have depth in addition to
width and height. Some common simple space figures include cubes, spheres,
cylinders, prisms, cones and pyramids. Let us discuss each of them in more
detail below.

1. Cube—Thisisa three-dimensional figure having six matching square
sides. An example of this isa box.

2. Cylinder—This isa space figure having two congruent circular bases
that are parallel. An example of this isa pitcher or a drinking glass.

3. Sphere—This isa space figure having al ofits points the same
distance from its center. An example ofthis is a basketball

2

26. 4. Cone—This is a space figure having a circular base and a single
vertex. An example of this is an ice cream cone,

A

5. Pyramid—This is a space figure with a square base and four
triangular-shaped sides. Examples ofthis are the pyramids you can
see in Egypt

D

6. Tetrahedron—This is a four-sided space figure. Each of it faces is
2 triangle. An example of this isthe Tetra Pak some commercial fruit
Juices like Zip use.

D

a

27. 7. Prism—Thisis a space figure with two congruent parallel bases that
are polygons. The most common kind ofthis figure is the triangular
prism. An example ofthis is the box that Toblerone is kept in.

Py Let's Try This

‘Think of other common things that are shaped like the space figures you
just leamed about, List five of them down in the spaces provided below
indicating their corresponding shapes.

1

Have your instructional Manager check your answers. Ask hinvherto give
you some feedback before going to the next part of the lesson.

28. 2 Let's See What You Have Learned

Match the pictures in Column A with their names in Column B by drawing
‘connecting lines.

Column A Column B

Sphere

9 Teraheon
O) Cylinder

‘Triangular prism

Cube

D
AZ

Cone

23

29. Compare your answers with those in the Answer Key on pages 30 and 31
Did you get all the answers right? If you did, that’s very good. You may then
proceed to the next part of the module. If you didn’t, don’t worry. Just review
the parts of the lesson you made mistakes in before going to the next part of
the module,

a Let's Remember
+ The most common space figures include the following:
1. cubes
2. cylinder;
3. sphere;
4. cone;
5. pyramid;

6. tetrahedron; and
7. prism,
Well, this is the end of the module! Congratulations for finishing it. Did

you like it? Did you learn anything useful from it? A summary of its main
points is given below to help you remember them better.

E Let's Sum Up

‘This module tells us that:

+ Aline has no definite beginning and end.
‘+ The two basic types of lines are straight and curved lines.

+ There are three kinds of straight lines—parallel, intersecting and
perpendicular lines.

+ The term congruence refers to the state of agrecing or coinciding.

2

30. ‘+ The four basic kinds of angles are acute, right, obtuse and straight
angles

+ Themostcommon plane figures include he following:

1. trapezoid;
2. parallelogram;
3. rhombus;

4. rectangle;
5. square;
6. wiangle;
7. pentagon;
8. hexagon;
9. octagon;

10. circle; and

11, oblong.

‘+ The most common space figures include the following:

1. cube;

2. cylinder;
3. sphere;
4. cone;

5. pyrami

6. tetrahedron; and

7. prism,

25

31. & What Have You Learned?

Complete the following crossword puzzle using the given clues.

10.

fo

E

Across

Lines that do not and will not
ever intersect

A space figure having all of
its points the same distance
from its center

A quadrilateral having only
two sides parallel

Athree-dimensional figure
having six matching square
sides

A space figure with two
‘congruent, parallel bases
that are polygons

26

Down

An angle which measures less
than 90°

Lines that forma 90°-angle
when they intersect

A parallelogram with four
equal sides and no right
angles

‘A quadrilateral with opposite
sides parallel and equal

Lines that cross each other at
a certain point

A polygon having six sides

32. 12. Arectangle withall four
sides equal

13. Aspace figure having all of
its points the same distance
from its center

14. A space figure having two
congruent circular bases that
are parallel

15. Anangle which measures
exactly 90°

Compare your answers with those in the Answer Key on page 31. How
well did you do?

2

33. Y Answer Key

A. Let's See What You Already Know (pages 1-2)
AL

mas

»

B. Lesson 1
Lets Review (page 6)
Pe
Pa
1
Pe
Pa

Lets Try This (page 9)
1. obtuse

2. acute
3. right
4. straight
5. right

2

34. Lets See What You Have Learned (page 10)

24
3 a
4 e
Se
6 b
Th
8 ©
% ©
10. i
Lesson 2

Lets Think About This (pages 12-13)

1. trapezoid
2. pentagon
3. square

4. triangle

5. rectangle
6. circle

7. oblong
8. hexagon
9. rhombus
10. octagon

»

35. Let's See What You Have Learned (pages 17-18)

on so

9 €
10.

Lesson 3

Lets See What You Have Learned (pages 23-24)

7

| —— Cube

———> Cyiinder

a
a
A

—— Cone

30

36. PS =

Tetrahedron

D —

>» Triangular prism

E. What Have You Learned? (pages 26-27)

F4

G

PsfP|H]EPRIE

[FIR [1 [sm

Psfalulalrle

D

R

E

ı In[olelr

L

Saca

felulsle

Fa

KONG

"rIrlalelelzlofı

[eRalrlaltlelelı

a

37. u References

Integrated Publishing. (1998). Chapter 17: Plane Figures. bup:l!
www. pub comimath]/18,htm. August 28, 2001, date accessed.

Joyce, D.F. (1996). Euclid s Elements Book I. Clark University. hitp:/!

Jarku.edu/-djoyce/iav: okl.html. August
28, 2001, date accessed.

Lesson Two: The Area of Rectangles. htipu/swww.icubed.com/
TE 121/Tessontwo,htm. August 28, 2001, date accessed,

Lines and Angles. bitp:/practice satmath.com/sat /tutoria)/section10/
pLhiml. August 28, 2001, date accessed.

Loy, Jim. (1997). Congruence of Triangles. hiz//wws.men.nev-jreloy/
‘congruen.htm. August 28, 2001, date accessed.

Motyka, Mark. (2001). Space Figures and Basic Solids. Math League

Multimedia. htp/Avwnw mathleague.combelp/geometry/3space.him.
August 28, 2001, date accessed.

E

38. Conversion Tables:

English to Metrie
To Change Te Nu By
inches Milimetrs 254
inches Cenineres 25
Inches Meter 0254
Fest Motes 03018
Mies Kitomatss 1609347
Square inches Square enincien 6452
Square fet Square meters 00929
Cbs inches Cub contimeter 163872
Cube feet, Cab meters ‘002832
Pounds Kilogams 045359
Ounces (avoiedpois) Grams 253995
Pounds pe quae inch Kilogram per square centimes 0005
Tom Kilograms 907.188
- Metri to English

To Change To Map By
Mimet Inches 003957,
Cemimetes Inches 0397
Mates Inches wx
Meter Fest 3281
Kilometers Mies van
Square centimeters Square inches 01550
Saure motes Square fs 107649
Cave centimeters (Cubic inches 6.061
Cubie meters Cie fe ssid
Kilogams Pounds 22046
Gras Ounces (voidupois) 003527
Kilograms per square centimeter Pounds pr agus inch 14223

Lupang Hinirang

Daga ie
Pre Sango,
Akne so,

Sacado muy by,

Se muelle
Dita pa,

SE smoy art ng mong bug,
ay lo ag a

‘Aisa poglya nama
Arg kp ng wast y
Kan qa ma y pi,
gta pe

[” Philippine Nationa Flag

Symbolism

Dive
Red
Equittra rangle
igh ea of he sua

Three stars

spook Le

”
oa, truth and justice
Ptit and coma
equal “
Fi lg provinces to evo prit Spin |
Masia, Laguna, Pampanga, Caio,

Bulacan, Nuova Bein Batangas & Tae)
tre mor island groupe (Lazos, Vas |
and Mindanao} |”

39. “Tre Baron of Nonermal Education, Phiipines was amer

ra ARB) system.

The international sitio of the significance and fre af be
urea in making ao accenible tosco fit sindecd an
Education, Culture and Sports

or no only 9 the Depariment
ut at he entire Filipino nation

Secret Genet
UNESCO National Commision of the Philippines