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DEPARTMENT OF EDUCATION DIVISION OF SAN JOSE DEL MONTE CITY San Ignacio St., Poblacion, City of San Jose del Monte, Bulacan 3023

Mathematics Quarter III – Module 1 Basic Concepts in Geometry and Kinds of Angles

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Mathematics - Grade 7 Alternative Delivery Mode Quarter 3-Module 1: Basic Concepts in Geometry and Kinds of Angles

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7 Mathematics Quarter III – Module 1 Basic Concepts in Geometry and Kinds of Angles

Department of Education • Republic of the Philippines

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. 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. Thankyou.

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What I Need to Know CONTENT STANDARD The learner demonstrates understanding of the key concepts of geometry of shapes and sizes and geometric relationships. PERFORMANCE STANDARD The learner is able to create models of plane figures and formulate and solve accurately authentic problems involving sides and angles of polygon. MOST ESSENTIAL LEARNING COMPETENCIES • • •

The learner represents point, line and plane using concrete and pictorial models. The learner illustrates subsets of a line. The learner classifies the different kinds of angles.

At the end of this module, learners are expected to: 1. 2. 3. 4.

represent point, line and plane using concrete and pictorial models; illustrate the different subsets of a line; name a point, line and plane and the different subsets of a line; and, classify the different kinds of angles.

What I Know Before proceeding to our lesson in this module, let us first check your prior knowledge for this topic. Answer the questions that follow on a separate sheet of paper. Choose the letter of your answer. 1. Which is NOT an undefined term in geometry? A. angle B. line C. plane 2. What is used to name a point? A. one cursive lowercase letter B. one lowercase letter

D. point

C. one cursive uppercase letter D. one uppercase letter

3. Which has no width but has a length and extends indefinitely on both sides? A. angle B. line C. plane D. ray

1

For nos. 4 and 5, refer to the figure below:

.A

A.

.C 4. 5.

X

.H

What term is illustrated by the figure shown above? A. angle B. line C. plane

D. segment

Which is the correct name of the figure? A. Line AC B. Point C C. Plane CXH

D. Plane X

6.

Which is a subset of a line that has one endpoint and extends indefinitely on one side? A. angle B. line C. line segment D. ray

7.

Which is a subset of a line which has two endpoints. A. angle B. line C. line segment

D. ray

Which illustrates a ray? A. B.

C.

D.

Which shows a line segment? A. B.

C.

D.

8.

9.

10. The figure for ray AB is this B . Which is wrong in the preceding A statement? A. The figure is not a ray, it is a line segment. B. The name should be line AB and not ray AB. C. The name should be ray BA and not ray AB. D. The figure has only one endpoint, so it is not a ray. 11. An angle that measures less than 90๐ but more than 0๐ is a/an __________. A. acute angle B. obtuse angle C. right angle D. straight angle 12. If m∠ABC is 130o, then it is a/an _______. A. acute angle B. obtuse angle C. right angle 13. Which of the following figure shows an acute angle? A. B. C.

14. 15.

D. straight angle D.

An angle whose measure is exactly 90o is a/an _______. A. acute angle B. obtuse angle C. right angle

D. straight angle

What instrument is used to measure an angle? A. compass B. measuring tape C. protractor

D. ruler

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LESSON

Undefined Terms in Geometry

1

What’s In

This module marks the start of another chapter on our lessons in Mathematics for Grade 7 learners. For the entire quarter, we will be discussing topics about Geometry – the branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids. I am sure you already have an idea about Geometry since this topic is also discussed on lower grade levels. To check your previous knowledge, answer the activity below. Directions: The array of letters below includes ten basic geometric terms including the two words already marked. These words are arranged horizontally, vertically, and diagonally. On a separate piece of paper, list down all the geometric terms that you can find.

A X P N R Z A B

N A L E A I C S

G B A W Y I E O

L I N E R G Q L

E C E C M W A I

C V L E A E C D

1. ______ CIRCLE ______ 2. _____ POLYGON _____ 3. ____________________ 4. ____________________ 5. ____________________

D E N Q A R U S

E T P R I T T C

P O I N T Y E D

P O L Y G O N Y

6. ___________________ 7. ___________________ 8. ___________________ 9. ___________________ 10. __________________

Good job! I know you did well in finding the geometric terms! You can now proceed to answering the next activity. 3

What’s New For this section, we will be having another activity! Group the following phrases into three groups according to their similarities. Specify the similar characteristic per group. Copy and answer this activity on a separate sheet of paper. a dash of salt the top of a table the tip of an umbrella the surface of the blackboard

the tip of a pencil the edge of the page of a book the floor of the classroom the edge of a ruler

Group 1

Group 2

Group 3

Similar Characteristics:

Similar Characteristics:

Similar Characteristics:

_____________

_____________

_____________

(a)

Which among the groups can you determine possible representations of a point?

(b)

Which among the groups can you determine possible representations of a line?

(c)

Which among the groups can you determine possible representations of a plane?

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What is It Undefined Terms in Geometry There are three basic terms in geometry which we refer to as undefined terms. These are point, line, and plane. We classify these as undefined terms because the definitions of these terms are not precise. Instead, we use representations to describe them. Undefined Representation Term

Point

Dot ·

How to Name/Denote

Capital letter ·W Read as: Point W

Line

Straight mark with two arrow heads

Other Information • It is a location in space with no dimension. • It has no length, width, or thickness.

Labeled with a single lowercase letter or it can also be labeled with two capital letters, • It has no representing the thickness, two distinct points but its on the line. length D E extends infinitely to n both directions. Denotations: DE - read as line DE ED - read as line ED ℓn - read as line n

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Real-Life Example • tip of a pen

• It is straight.

• line guides on intermediate papers

Slanted foursided figure

Plane

Single capital script letter or by • It has no three noncollinear thickness points extends indefinitely P in all ·Y directions. ·X ·Z Read as: Plane XYZ or Plane P

• flat-panel television screen

• It is a flat surface.

What’s More Let us check what you have learned from the previous section of this module. Try answering the following activities on a separate sheet of paper. A. Identify whether the object is a representation of a point, line, or plane. 1. cellphone screen

__________________

2. edge of a wall

__________________

3. grain of salt

__________________

4. strand of straight hair

__________________

5. tip of a crayon

__________________

B. Illustrate each of the following and label the diagram. 1. point B lies in plane M

__________________

2. line CD

__________________

3. point A

__________________

4. point F

__________________

5. line AT

__________________

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LESSON

Subsets of a Line

2

What’s In Before we proceed, let us have a review about the previous lessons by answering the given activity below. Refer to the figure at the right to answer the questions that follow. B 1. Name all the lines. F 2. Name all the segments. 3. Name all the rays. G C

What’s New It looks like you already mastered the two previous lessons. Now consider the situation described below. The SPA Grade 7 students of Sapang Palay National High School will perform a dance number for their culminating ac s to incorporate the arm gesture that eography. The arm

H

R

R B

M

C

A

J

T

L

D

G

Process Questions: 1. Suppose the arms represent a ray, name all the rays from the figure. 2. What have you observed on the rays on the figure? 3. What is formed when two rays are joined with a common endpoint? 7

What Is It Were you able to answer the third question? Well, the answer is our lesson for this section – Angle! An angle is defined as a figure formed by two rays having the same endpoint not lying on the same line. It is denoted by the symbol ∠. In the figure below, the two rays EB and ET are called the sides of the angle and their common endpoint (point E) is called the vertex of the angle. The angles can be called ∠E, ∠ BET or ∠TEB. If three letters are used to name an angle, the middle letter denotes the vertex. B

E

T

Angles are classified according to their measurement. A protractor is used to measure angles. An angle’s unit of measurement is in degrees (0). We can classify angles into four, namely: acute angle, right angle, obtuse angle, and straight angle. Consider the following illustrative examples of each. I The measure of ∠IOU is 500, therefore the angle is an acute angle.

O Figure 1

U

An acute angle is an angle that measures greater than 00 but is less than 900.

E The measure of ∠EFG is 900, therefore it is a right angle. A right angle is an angle that is equal to 900. F Figure 2

G

8

K

The measure of ∠KLN is 1300, therefore it is an obtuse angle.

L

N

An obtuse angle is an angle that is greater than 900 but is less than 1800.

Figure 3

The measure of ∠RQS is 1800, therefore it is a straight angle. Q

R

S

A straight angle is an angle that is equal to 1800.

Figure 4

Familiarizing yourself on using the protractor will be helpful in classifying angles. So, this is an additional helpful Information for you! How to use protractor: 1. Place the center point of the protractor on the vertex of the angle to be measured. 2. Make sure that the mark labeled 0 on either score is placed on one side of the angle. 3. Read the scale where the other side of the angle falls.

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What’s More A. Given the figures below, classify each as acute, right, obtuse, or straight angle. Verify your answer by measuring each figure using a protractor. Write your answer on a sheet of paper.

1.

2.

_______________

`

_______________

3.

4.

_______________

_______________

5.

_______________ B. Classify the angle given the following angle measures. Write your answer on a piece of paper. 1.

360

2.

1000

3.

1800

4.

900

5.

1760

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What I Have Learned You finished three lessons for this module! Good Job! Now, let us check what you remembered from the lessons by completing the following concept maps.

Undefined Terms in Geometry

Illustration

Illustration

Illustration

Subsets of a Line

Illustration

Illustration

Classifications of Angles

Illustration

Illustration

Illustration

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Illustration

What I Can Do Points, lines, planes, line segment, ray, and angle represent some of the fundamental building blocks of all geometry. Your task for this section of the module is to draw or cut out a picture (this can be taken from a magazine or from the internet) that represents each of the terms. Each real-world picture should include a caption to identify which aspect of the picture represents the term. Do this on a separate sheet of paper. Refer to the sample layout below. Name: (Paste or draw here the real-world picture of the geometric term)

Point

(Caption) (Paste or draw here the real-world picture of the Line

geometric term) (Caption) (Paste or draw here the real-world picture of the geometric term)

Plane

(Caption) (Paste or draw here the real-world picture of the Line Segment

geometric term) (Caption) (Paste or draw here the real-world picture of the

Ray

geometric term) (Caption) (Paste or draw here the real-world picture of the

Angle

geometric term) (Caption)

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Assessment Directions: Choose the letter of your answer and write it down on a separate sheet of paper. 1. Which is an undefined term in geometry? A. angle

B. line segment

C. plane

D. ray

2. What is used to name a line? A. two cursive lowercase letter

C. two cursive uppercase letter

B. two lowercase letter

D. two uppercase letter

3. Which has width and length that extends indefinitely in all directions? A. angle

B. line

C. plane

D. ray

For nos. 4 and 5, refer to the figure below: T

B

4. What geometric term is illustrated by the figure shown above? A. line

B. point

C. plane

D. segment

5. Which is the correct name for the figure? A. Angle BT

B. Line BT

C. Plane BT

D. Point B

6. Which is a subset of a line that has two endpoints? A. angle

B. line

C. line segment

D. ray

7. Which is a subset of a line that has one endpoint and extends indefinitely on one side? A. angle

B. line

C. line segment

D. ray

C.

D.

C.

D.

8. Which illustrates a line segment? A.

B.

9. Which illustrates a ray? A.

B.

13

10. The figure for ray FE is this E

F

. Which is wrong in the statement?

A. The figure is not a ray, it is a line segment. B. The name should be ray EF and not ray FE. C. The figure has only one endpoint, so it is not a ray. D. There is nothing wrong in the statement. 11. An angle that measures more than 90๐ but less than 180๐ is a/an _________. A. acute angle

B. obtuse angle

C. right angle

D. straight angle

12. Which is an angle whose measure is exactly 90o? A. acute angle

B. obtuse angle

C. right angle

D. straight angle

13. If m∠ABC is 80o, then it is a/an _______. A. acute angle

B. obtuse angle

C. right angle

D. straight angle

14. Which of the following figure shows a straight angle? A.

B.

C.

D.

15. If m∠Y is 91o, then it is a/an _______. A. acute angle

B. obtuse angle

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C. right angle

D. straight angle

Additional Activities You are almost done answering this module! For the last activity, complete this crossword puzzle. Write your answer on a separate sheet of paper. Basic Concepts on Geometry

Across 1. subset of a line which starts at a point and extends in a particular direction to infinity 6. subset of a line that has two endpoints 8. angle that measures more than 900 but less than 1800 11. angle that measures exactly 900 12. representation of a point Down 2. angle that measures less than 900 but more than 00 3. a flat surface 4. instrument used to measure an angle 5. it is the common endpoint of two rays that form an angle 6. it has no width and extends indefinitely on both sides 7. this can be denoted using a single capital letter 9. angle that measures exactly 1800 10. it is formed by two rays with common vertex

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16 Lesson 2: What’s In

What I Know: 1. A 2. D 3. B 4. C 5. D 6. D 7. C 8. D 9. B 10. C 11. A 12. B 13. B 14. C 15. C Lesson 1: What’s In

LINES Stick Ruler

POINTS

Ball Button Coin

(Answers may vary) (Answers may vary) What’s More Activity 1 തതത or DR തതതതത A. 1. തത RD ሬሬԦ 2. ሬሬሬ TA ሬሬሬԦ 3. ሬሬሬ RM ത ത തതത or തGS തതതത 4. SG ሬԦ 5. ሬሬሬሬ MJ B. 1. 2.

What’s New (Answers may vary) What’s More: A. 1. plane 2. line 3. point 4. line 5. point

3.

B. 1.

5. Activity 2

5.

M

4.

LINE SE...