# Lines, Bearing and Angles : How to draw and identify parallel lines and Perpendicular lines Primary 5 Third Term Lesson Notes Mathematics Week 2

**Subject : Mathematics **

Class :Primary 5

Term : Third Term

Week :Week 2

Topic : Lines, Bearing and Angles : How to draw and identify parallel lines and Perpendicular lines

Previous Lesson : Temperature Primary 5 Third Term Lesson Notes Mathematics Week 1

Content :

### Lines, Bearing and Angles : How to draw and identify parallel lines and Perpendicular lines

Good morning, class! Today, we’re going to learn about lines, bearings, and angles. Specifically, we’ll focus on drawing and identifying parallel lines and perpendicular lines. So let’s get started!

First, let’s talk about lines. A line is a straight path that extends infinitely in both directions. It has no endpoints. We can represent a line with a straight line segment and use arrows on both ends to show that it continues infinitely.

Now, parallel lines are lines that never intersect or cross each other. They always remain the same distance apart. When we draw parallel lines, it’s important to make sure the distance between them remains equal throughout.

To draw parallel lines, you can start by drawing one line segment. Then, using a ruler, place it next to the first line segment. Make sure the ruler is parallel to the first line segment. Without changing the angle of the ruler, draw another line segment. Remember to extend the lines indefinitely, and you’ll have two parallel lines!

Now, let’s move on to perpendicular lines. Perpendicular lines are lines that intersect or cross each other at a 90-degree angle, forming right angles. When we draw perpendicular lines, we want to make sure the angles they form are all right angles.

To draw perpendicular lines, we can start by drawing one line segment. Then, using a protractor, measure a 90-degree angle at the endpoint of the first line segment. Place the protractor’s baseline along the endpoint of the first line segment, and align the 90-degree mark with the line segment. Draw the second line segment along the edge of the protractor. The two lines will be perpendicular to each other, forming right angles where they intersect.

Now, let’s quickly review how to identify parallel lines and perpendicular lines. When looking at a pair of lines, we can determine if they are parallel by checking if they never intersect and if the distance between them remains the same. On the other hand, if two lines intersect at a 90-degree angle, they are perpendicular.

Remember, when identifying parallel lines or perpendicular lines, it’s important to closely observe the angles formed and how the lines relate to each other.

Alright, class! That’s all for today’s lesson on drawing and identifying parallel lines and perpendicular lines. I hope you found it informative. Now it’s time for some practice! Let’s work on some exercises to reinforce what we’ve learned.

Triangle Properties

The properties of the triangle are:

- The sum of all the angles of a triangle(of all types) is equal to 1800.
- The sum of the length of the two sides of a triangle is greater than the length of the third side.
- In the same way, the difference between the two sides of a triangle is less than the length of the third side.
- The side opposite the greater angle is the longest side of all the three sides of a triangle.
- The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property
- Two triangles are said to be similar if their corresponding angles of both triangles are congruent and lengths of their sides are proportional.

Area of a triangle = ½ × Base × Height

The perimeter of a triangle = sum of all its three sides

**Evaluation**

- Two lines that never intersect and always remain the same distance apart are called __________. a) Parallel lines b) Intersecting lines c) Perpendicular lines d) Vertical lines
- To draw parallel lines, you need to make sure the distance between them remains __________. a) Different b) Increasing c) Decreasing d) Equal
- Perpendicular lines form ________ angles where they intersect. a) Acute angles b) Obtuse angles c) Right angles d) Straight angles
- When drawing perpendicular lines, the angle formed at the intersection should be ________ degrees. a) 45 b) 90 c) 180 d) 360
- Two lines that intersect at a 90-degree angle are ________ lines. a) Parallel b) Vertical c) Perpendicular d) Diagonal
- If two lines are perpendicular, the product of their slopes is ________. a) 0 b) 1 c) -1 d) Undefined
- When identifying parallel lines, it’s important to check if they ________. a) Intersect b) Are curved c) Remain the same distance apart d) Have different lengths
- A straight path that extends infinitely in both directions without any endpoints is called a ________. a) Line segment b) Ray c) Line d) Angle
- To draw parallel lines, we can use a ________ to keep the distance between the lines equal. a) Compass b) Protractor c) Ruler d) Calculator
- Perpendicular lines can be identified by checking if they intersect at a ________ angle. a) 45-degree b) 90-degree c) 180-degree d) 360-degree

(a) equilateral

-All sides are equal

-All angles are equal

(b) isosceles

-Two opposite side are equal

-Two base angles are equal

(c) scalene

-The three sides are not equal

-The three angles are not equal

d). Right angled:

-Two sides are perpendicular

-One angle is a right angle

(I). Parallelogram

-Opposite sides are equal

-Opposite sides are parallel

(II). Trapezium

-One pair of opposite sides are Parallel

-No line of symmetry

Rhombus

-All sides are equal

-Opposite angles are equal

-Has two lines of symmetry

-Diagonals are perpendicular to Each other

(II). Square

-All sides are equal

-All angles are equal

-Diagonals meet at angles 90Right angle

-Has four lines of symmetry

(III). Rectangle

-Opposite sides are equal and

Parallel

-All angles are equal

-Has two lines of symmetry

WEEK 4

Topic: Angles

Complementary Angle

Two Angles are Complementary when they add up to 90 degrees (a Right Angle).

They don’t have to be next to each other, just so long as the total is 90 degrees.

Examples:

- 60° and 30° are complementary angles.
- 5° and 85° are complementary angles.

Supplementary Angles

Two Angles are Supplementary when they add up to 180 degrees.supplementary angles 40 and 140

These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:Notice that together they make a straight angle. supplementary angles 60 and 120But the angles don’t have to be together.

These two are supplementary because 60° + 120° = 180°

Acute angle:

An angle whose measure is less than 90 degrees.

Right angle

angle whose measure is 90 degrees.

Obtuse angle:

An angle whose measure is bigger than 90 degrees but less than 180 degrees. Thus, it is between 90 degrees and 180 degrees.

Straight angle

An angle whose measure is 180 degrees.Thus, a straight angle look like a straight line.

Reflex angle:

An angle whose measure is bigger than 180 degrees but less than 360 degrees.

In worksheet on angles you will solve 10 different types of questions on angles.

- Classify the following angles into acute, obtuse, right and reflex angle:

(i) 35°

(ii) 185°

(iii) 90°

(iv) 92°

(v) 260°

- Measure these angles:
- Use your protractor to draw these angles:

(i) 40°

(ii) 125°

(iii) 25°

- Identify which of the following pairs of angles are complementary or supplementary?

(i) 70°, 20°

(ii) 20°, 170°

(iii) 50°, 145°

(iv) 125°, 55°

(v) 105°, 75°

(vi) 55°, 35°

- Find the complement of each of the following angles:

(i) 40°

(ii) 27°

(iii) 35°

- Find the supplement of each of the following angles?

(i) 100°

(ii) 90°

(iii) 110°

(iv) 107°

- Draw a pair of supplementary angles such that one of them measures:

(i) 120°

(ii) 90°

- Construct the angles of the following measures with the help of a compass:

(i) 150°

(ii) 90°

(iii) 120°

- An angle whose measure is less than 90° is called an ……………… .
- An angle measure 0° is called a …………….. .

Lesson 2

### Lines, Bearing and Angles : How to draw and identify complementary angles and Supplementary angles using protractor

Good morning, class! Today, we’re going to learn about lines, bearings, and angles. Specifically, we’ll focus on how to draw and identify complementary angles and supplementary angles using a protractor. So let’s get started!

First, let’s review what angles are. An angle is formed when two lines or line segments meet at a common endpoint, which we call the vertex of the angle. We use a protractor to measure and draw angles accurately.

Complementary angles are a pair of angles that add up to 90 degrees. To draw complementary angles using a protractor, follow these steps:

1. Start by drawing a straight line segment.

2. Place the protractor on the line segment, aligning its baseline with the line.

3. Locate the vertex of the angle at one end of the line segment.

4. Find the 90-degree mark on the protractor and make a small dot or mark on the paper at that point.

5. Without moving the protractor, draw a line from the vertex to the dot you marked. This will be the first angle.

6. Measure the angle you just drew using the protractor to make sure it is 90 degrees.

7. To draw the complementary angle, place the protractor on the other side of the line segment, again aligning its baseline with the line.

8. Repeat steps 3 to 6 to draw the second angle, making sure it also measures 90 degrees.

Supplementary angles, on the other hand, are a pair of angles that add up to 180 degrees. To draw supplementary angles using a protractor, follow these steps:

1. Start by drawing a straight line segment.

2. Place the protractor on the line segment, aligning its baseline with the line.

3. Locate the vertex of the angle at one end of the line segment.

4. Find the 180-degree mark on the protractor and make a small dot or mark on the paper at that point.

5. Without moving the protractor, draw a line from the vertex to the dot you marked. This will be the first angle.

6. Measure the angle you just drew using the protractor to make sure it is 180 degrees.

7. To draw the supplementary angle, place the protractor on the other side of the line segment, again aligning its baseline with the line.

8. Repeat steps 3 to 6 to draw the second angle, making sure it also measures 180 degrees.

Now, let’s quickly review how to identify complementary angles and supplementary angles. When you have two angles, if they add up to 90 degrees, they are complementary. If they add up to 180 degrees, they are supplementary.

Alright, class! That’s all for today’s lesson on drawing and identifying complementary angles and supplementary angles using a protractor. I hope you found it informative. Now it’s time for some practice! Let’s work on some exercises to reinforce what we’ve learned.

**Evaluation**

- Complementary angles are a pair of angles that add up to ________ degrees. a) 45 b) 90 c) 180 d) 360
- To draw complementary angles using a protractor, you need to make sure each angle measures ________ degrees. a) 45 b) 90 c) 180 d) 360
- Supplementary angles are a pair of angles that add up to ________ degrees. a) 45 b) 90 c) 180 d) 360
- When using a protractor to draw supplementary angles, each angle should measure ________ degrees. a) 45 b) 90 c) 180 d) 360
- Complementary angles can be identified when their sum is equal to ________ degrees. a) 45 b) 90 c) 180 d) 360
- To draw complementary angles using a protractor, you need to draw ________ angles on the same line. a) Two acute b) Two obtuse c) One acute and one obtuse d) Two right
- Supplementary angles can be identified when their sum is equal to ________ degrees. a) 45 b) 90 c) 180 d) 360
- When using a protractor to draw supplementary angles, you need to draw ________ angles on the same line. a) Two acute b) Two obtuse c) One acute and one obtuse d) Two right
- If one angle measures 45 degrees, its complementary angle will measure ________ degrees. a) 45 b) 90 c) 135 d) 180
- If one angle measures 100 degrees, its supplementary angle will measure ________ degrees. a) 45 b) 90 c) 100 d) 180

Lesson 3

### Lines, Bearing and Angles : How To Calculate the complementary, opposite, Supplementary angles by telling the direction accurately using angles in real life situation

Good morning, class! Today, we’re going to dive into the topic of lines, bearings, and angles, focusing on how to calculate complementary angles, opposite angles, and supplementary angles. We’ll also explore how angles are used to describe directions accurately in real-life situations. So let’s get started!

First, let’s review some important terms related to angles. An angle is formed when two lines or line segments meet at a common endpoint, called the vertex. Angles are measured in degrees using a protractor. Now let’s move on to the different types of angles we’ll be discussing.

Complementary angles are a pair of angles that add up to 90 degrees. To calculate the measure of a complementary angle, you subtract the given angle from 90 degrees. For example, if one angle measures 45 degrees, the complementary angle will be 90 – 45 = 45 degrees. The sum of these two angles will always be 90 degrees.

Opposite angles are formed when two lines intersect. They are opposite each other and have equal measures. For example, if you have two intersecting lines, the angles across from each other will be equal. This property is important when working with shapes like parallelograms or when using the concept of symmetry.

Supplementary angles are a pair of angles that add up to 180 degrees. To calculate the measure of a supplementary angle, you subtract the given angle from 180 degrees. For instance, if one angle measures 100 degrees, the supplementary angle will be 180 – 100 = 80 degrees. The sum of these two angles will always be 180 degrees.

Now, let’s explore how angles are used to describe directions accurately in real-life situations. In navigation or compass bearings, angles are used to indicate directions. The four main cardinal directions are North, South, East, and West, with North being 0 degrees or 360 degrees. Using angles, we can describe directions in between these cardinal points. For example, if we want to go Northeast, we would use an angle of 45 degrees. Similarly, if we want to go Southwest, we would use an angle of 225 degrees.

By understanding angles and their measures, we can accurately communicate directions in various contexts, such as maps, compasses, or giving instructions for navigation.

Alright, class! That’s all for today’s lesson on calculating complementary angles, opposite angles, and supplementary angles, as well as using angles to describe directions accurately in real-life situations. I hope you found it informative. Now it’s time for some practice! Let’s work on some exercises to reinforce what we’ve learned.

**Evaluation**

**Example 1:**

Calculate the measure of the complementary angle of an angle measuring 40 degrees.

Solution: Complementary angle = 90 degrees – 40 degrees = 50 degrees

**Example 2:**

If angle A measures 30 degrees, what is the measure of its complementary angle?

Solution: Complementary angle = 90 degrees – 30 degrees = 60 degrees

**Example 3:**

In a parallelogram, if one angle measures 50 degrees, what is the measure of its opposite angle?

Solution: Opposite angles in a parallelogram are equal, so the opposite angle also measures 50 degrees.

**Example 4:**

Calculate the measure of the supplementary angle of an angle measuring 120 degrees.

Solution: Supplementary angle = 180 degrees – 120 degrees = 60 degrees

**Example 5:**

If angle B measures 80 degrees, what is the measure of its supplementary angle?

Solution: Supplementary angle = 180 degrees – 80 degrees = 100 degrees

**Example 6:**

In a rectangle, if one angle measures 70 degrees, what is the measure of its opposite angle?

Solution: Opposite angles in a rectangle are equal, so the opposite angle also measures 70 degrees.

**Example 7:**

A compass bearing of 270 degrees represents which cardinal direction?

Solution: A compass bearing of 270 degrees represents West.

**Example 8:**

To travel Northwest, what angle should be used?

Solution: Northwest is halfway between North and West, so the angle would be 315 degrees.

**Example 9:**

If a compass bearing is 120 degrees, what direction is being indicated?

Solution: A compass bearing of 120 degrees represents Southeast.

**Example 10:**

To travel Southwest, what angle should be used?

Solution: Southwest is halfway between South and West, so the angle would be 225 degrees.

**Evaluation**

1. Complementary angles add up to ________ degrees.

a) 45

b) 90

c) 180

d) 360

2. To calculate the complementary angle of an angle measuring 50 degrees, we subtract it from ________ degrees.

a) 45

b) 90

c) 135

d) 180

3. Opposite angles in a parallelogram have ________ measures.

a) Different

b) Equal

c) Supplementary

d) Complementary

4. In a rectangle, opposite angles have ________ measures.

a) Different

b) Equal

c) Supplementary

d) Complementary

5. Supplementary angles add up to ________ degrees.

a) 45

b) 90

c) 180

d) 360

6. To calculate the supplementary angle of an angle measuring 120 degrees, we subtract it from ________ degrees.

a) 45

b) 90

c) 135

d) 180

7. When giving directions using compass bearings, North is represented by ________ degrees.

a) 0

b) 45

c) 90

d) 180

8. To travel Southeast, we would use a compass bearing of ________ degrees.

a) 45

b) 90

c) 135

d) 180

9. A compass bearing of 270 degrees represents ________.

a) North

b) East

c) South

d) West

10. To travel Northwest, we would use a compass bearing of ________ degrees.

a) 45

b) 90

c) 135

d) 315

### Lesson Plan Presentation

Topic: Lines, Bearings, and Angles

Lesson Plan Presentation

Topic: Lines, Bearings, and Angles

Lesson 1: How to draw and identify parallel lines and perpendicular lines

Learning Objectives:

– Understand the concept of parallel lines and perpendicular lines.

– Learn how to draw parallel lines accurately.

– Learn how to draw perpendicular lines accurately.

– Identify parallel lines and perpendicular lines in real-life situations.

Embedded Core Skills:

– Critical thinking

– Problem-solving

– Geometry

– Spatial visualization

– Measurement and accuracy

Learning Materials:

– Ruler

– Pencil

– Paper

– Protractor (for perpendicular lines)

Presentation:

1. Introduction (5 minutes)

– Greet the students and provide an overview of the lesson.

– Explain the importance of understanding parallel and perpendicular lines.

2. Definition and Examples (10 minutes)

– Define parallel lines and perpendicular lines.

– Show visual examples of parallel and perpendicular lines.

– Discuss real-life examples where parallel and perpendicular lines can be found.

3. Drawing Parallel Lines (15 minutes)

Teacher’s Activities:

– Demonstrate how to draw parallel lines using a ruler.

– Explain the concept of equal distance between the lines.

Learners Activities:

– Students follow along and practice drawing parallel lines on their own.

4. Drawing Perpendicular Lines (20 minutes)

Teacher’s Activities:

– Explain the process of drawing perpendicular lines using a ruler and protractor.

– Demonstrate how to measure and mark a 90-degree angle accurately.

– Guide students in drawing perpendicular lines step-by-step.

Learners Activities:

– Students practice drawing perpendicular lines using a ruler and protractor.

5. Identifying Parallel and Perpendicular Lines (10 minutes)

Teacher’s Activities:

– Show images and diagrams of various lines.

– Discuss with students how to identify parallel lines and perpendicular lines in the given examples.

Learners Activities:

– Students participate in a class discussion and identify parallel and perpendicular lines.

6. Assessment (10 minutes)

– Distribute a worksheet or handout with exercises to assess students’ understanding.

– Monitor students’ progress and provide assistance if needed.

7. Conclusion (5 minutes)

– Summarize the key points covered in the lesson.

– Highlight the importance of parallel and perpendicular lines in geometry and real-life applications.

Lesson 2: How to draw and identify complementary angles and supplementary angles using a protractor

Learning Objectives:

– Understand the concept of complementary angles and supplementary angles.

– Learn how to draw complementary angles using a protractor.

– Learn how to draw supplementary angles using a protractor.

– Identify complementary angles and supplementary angles in real-life situations.

Embedded Core Skills:

– Critical thinking

– Problem-solving

– Geometry

– Measurement and accuracy

Learning Materials:

– Protractor

– Pencil

– Paper

Presentation: (Follow a similar structure as Lesson 1)

1. Introduction (5 minutes)

– Review the concept of angles and their measures.

– Explain the importance of understanding complementary and supplementary angles.

2. Definition and Examples (10 minutes)

– Define complementary angles and supplementary angles.

– Show visual examples of complementary and supplementary angles.

– Discuss real-life examples where these angles can be found.

3. Drawing Complementary Angles (15 minutes)

Teacher’s Activities:

– Explain the process of drawing complementary angles using a protractor.

– Demonstrate how to measure and mark a 90-degree angle accurately.

Learners Activities:

– Students follow along and practice drawing complementary angles using a protractor.

4. Drawing Supplementary Angles (15 minutes)

Teacher’s Activities:

– Explain the process of drawing supplementary angles using a protractor.

– Demonstrate how to measure and mark a 180-degree angle accurately using a protractor.

Learners Activities:

– Students practice drawing supplementary angles using a protractor.

5. Identifying Complementary and Supplementary Angles (10 minutes)

Teacher’s Activities:

– Show images and diagrams of various angles.

– Discuss with students how to identify complementary angles and supplementary angles in the given examples.

Learners Activities:

– Students participate in a class discussion and identify complementary angles and supplementary angles.

6. Assessment (10 minutes)

– Distribute a worksheet or handout with exercises to assess students’ understanding.

– Monitor students’ progress and provide assistance if needed.

7. Conclusion (5 minutes)

– Summarize the key points covered in the lesson.

– Reinforce the importance of complementary and supplementary angles in geometry and real-life contexts.

Lesson 3: How to calculate complementary, opposite, and supplementary angles by accurately describing directions using angles in real-life situations

Learning Objectives:

– Understand the concept of complementary, opposite, and supplementary angles.

– Learn how to calculate these angles using subtraction or addition.

– Apply angles to accurately describe directions in real-life situations.

Embedded Core Skills:

– Critical thinking

– Problem-solving

– Geometry

– Spatial visualization

– Measurement and accuracy

Learning Materials:

– Compass

– Maps (optional)

– Worksheets or handouts with real-life scenarios (directions, compass bearings, etc.)

Presentation: (Follow a similar structure as Lesson 1)

1. Introduction (5 minutes)

– Review the concept of angles and their measures.

– Introduce the connection between angles and accurately describing directions in real-life situations.

2. Complementary, Opposite, and Supplementary Angles (10 minutes)

– Review the definitions of complementary, opposite, and supplementary angles.

– Discuss how these angles relate to each other and their sum or difference.

3. Calculating Complementary, Opposite, and Supplementary Angles (20 minutes)

Teacher’s Activities:

– Explain the process of calculating complementary, opposite, and supplementary angles using addition or subtraction.

– Provide examples and guide students through the calculations step-by-step.

Learners Activities:

– Students practice calculating these angles independently and check their answers.

4. Describing Directions Using Angles (15 minutes)

Teacher’s Activities:

– Introduce real-life scenarios where angles are used to describe directions accurately, such as navigation, compass bearings, or map reading.

– Show maps or diagrams to support the explanations.

Learners Activities:

– Students actively engage in discussions and participate in activities related to describing directions using angles.

5. Assessment (10 minutes)

– Distribute a worksheet or handout with exercises to assess students’ understanding.

– Monitor students’ progress and provide assistance if needed.

6. Conclusion (5 minutes)

– Summarize the key points covered in the lesson.

– Highlight the practical applications of angles in describing directions accurately in real-life situations.

Evaluation Questions:

1. What are parallel lines?

a) Lines that intersect at a 90-degree angle

b) Lines that never intersect and remain the same distance apart

c) Lines that form acute angles

d) Lines that form obtuse angles

2. How can you draw parallel lines using a ruler?

a) By drawing two lines that are not straight

b) By drawing two lines that intersect

c) By drawing two lines that are equidistant throughout

d) By drawing two lines that are not parallel to each other

3. What is the measure of the complementary angle of an angle measuring 70 degrees?

a) 20 degrees

b) 70 degrees

c) 110 degrees

d) 180 degrees

4. How can you draw perpendicular lines using a protractor?

a) By measuring a 90-degree angle at the endpoint of one line

b) By measuring a 180-degree angle at the endpoint of one line

c) By measuring a 45-degree angle at the endpoint of one line

d) By measuring a 360-degree angle at the endpoint of one line

5. Define supplementary angles.

a) Angles that add up to 90 degrees

b) Angles that add up to 180 degrees

c) Angles that form right angles

d) Angles that never intersect

6. What is the measure of the supplementary angle of an angle measuring 120 degrees?

a) 40 degrees

b) 60 degrees

c) 90 degrees

d) 180 degrees

7. How can you calculate complementary angles?

a) By subtracting the given angle from 180 degrees

b) By subtracting the given angle from 90 degrees

c) By adding the given angle to 180 degrees

d) By adding the given angle to 90 degrees

8. In a rectangle, opposite angles are ________.

a) Congruent

b) Complementary

c) Supplementary

d) Acute angles

9. How can angles be used to describe directions accurately?

a) By measuring the degrees of rotation

b) By counting the number of angles in a shape

c) By determining the length of the lines

d) By adding up the angles in a shape

10. What is the compass bearing for South?

a) 0 degrees

b) 45 degrees

c) 90 degrees

d) 180 degrees

Conclusion:

In conclusion, understanding lines, bearings, and angles is crucial in various mathematical and real-life contexts. By mastering the concepts of parallel lines, perpendicular lines, complementary angles, supplementary angles, and using angles to describe directions accurately, students develop essential skills in geometry, problem-solving, and spatial visualization. Remember to practice drawing and identifying these angles and explore real-life applications to reinforce your understanding. Keep up the great work!