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Grade 9 GEOMETRY OF STRAIGHT LINES:

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DATE: ……………………………………….

TOPIC: GEOMETRY OF STRAIGHT LINES

CONCEPTS & SKILLS TO BE ACHIEVED:

By the end of the lesson learners should know and be able to write clear descriptions of the

relationship between angles formed:

Parallel lines cut by transversal

RESOURCES: DBE Workbook 1, Sasol-Inzalo book, Textbooks,

ONLINE RESOURCES

https://drive.google.com/open?id=1Qw6gZzmSxQ-ypsHmqx1LHnVbA2HsKX79

https://www.thelearningtrust.org/asp-treasure-box

MATHEMATICS

GRADE 9

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Grade 9 GEOMETRY OF STRAIGHT LINES:

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DAY 1: ACTIVITY 1

Teacher instructs learner: Warm Up (10 mins)

Why Warm Up before the start of a lesson?

(Additional information

for student and teacher)

a) Give an example of a pair of vertically opposite angles (draw) and describe how to find

the value of one angle when the other is given.

Example

Description

b) Give an example of adjacent supplementary angle pair and describe how to

find the value of one angle when the other is given.

Example

Description

Use prior-knowledge activities to help

connect to the why of the lesson, paint

a picture of where students are headed

in the lesson, and develop student

perseverance during the lesson (by

reminding them throughout the lesson

how chosen activities connect to the

learning outcomes).

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Grade 9 GEOMETRY OF STRAIGHT LINES:

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DAY 1 ACTIVITY 1 & 2 LESSON PRESENTATION/DEVELOPMENT (Suggested time: 20 minutes)

INTRODUCTION: GRADE 8 REVISION

STUDY THE FOLLOWING CONCEPTS TO FAMILIARISE YOURSELF WITH SOME

FUNDAMENTALS:

What are Parallel Lines?

Two lines are parallel to each other if they are the same distance apart on each

point and never intersect each other.

Symbol (‖)

Parallel lines are indicated by using arrows on the lines.

Example:

∴ 𝑙𝑖𝑛𝑒 1 𝑖𝑠 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑙𝑖𝑛𝑒 2 ∴ 𝒍𝟏 ‖ 𝒍𝟐

Parallel lines in our daily life

Transversal: How do we define a transversal?

A transversal is a line that cuts or intersects 2 or more lines. The lines can be parallel or non –

parallel.

Example:

Transversal lines in our daily life:

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Grade 9 GEOMETRY OF STRAIGHT LINES:

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CONSOLIDATION/CONCLUSION

Activity 2: Copy and complete in your workbook.

Definition

Characteristics

Example (draw)

Definition

Characteristics

Example(draw)

Memorandum:

Day 1: Activity 1 & 2

Activity 1

a)

Example

Description

AB and CD intersect at O,

then O1 = ��2 and O3 = ��4

Parallel lines

Transversal line

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Grade 9 GEOMETRY OF STRAIGHT LINES:

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b)

Example

Description

1 2ˆ ˆIf ABC is a straight line, then B B 180

Activity 2

Definition

Two lines are parallel to each

other if they are the same distant

apart on each point and never

intersect each other.

Characteristics

Same distance apart

Never intersects

Moves in same direction

Indicates with arrows

Symbol (‖)

Example

Definition

A transversal is a line that cuts

or intersects 2 or more lines.

The lines can be parallel or non

– parallel.

Characteristics

Straight line

Creates 8 angles when it cut/

intersects pair of lines

Example

Parallel lines

Transversal line

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DAY 2 & 3: ACTIVITIES 3 - 6: LESSON PRESENTATION/DEVELOPMENT

Warm Up: Work through the exercise and complete the answers in your exercise book

Fill in the missing words

1.Parallel lines are two lines that are always the same __________ apart and never

________________.

2. A ____________________ is a line that intersects two lines at two different points.

3. When a transversal cut a set of parallel lines, ____________ angles are formed.

NOTE THE FACTS FOR TODAY’S LESSON:

a. What are exterior angles? (angles that lie on the outside of the parallel

lines cut by the transversal.) - ∠1 , ∠2 , ∠ 7 and ∠ 8

b. What are interior angles? (angles that lie between the

parallel lines cut by the transversal.) - ∠3 , ∠4 , ∠ 5 and ∠6

Activity 3:

Use tissue paper and color pencils in this activity to discover

alternate interior angles when a transversal cuts two parallel lines.

PART 1: INSTRUCTIONS:

On the picture below, using any colour pencil or highlighter, highlight parallel lines m

and n.

To answer the questions below rotate the tissue paper and place the angle you trace

on top of other angles to find matching angles.

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Focusing on the angles located between(interior area) parallel lines m and n. Place the tissue

paper on top of the picture

3.1 Trace angle 3

3.1.1 Find the angle equal to angle 3.

Colour both angles with the same colour

3.2 Trace angle 4

3.2.1 Find the angle equal to angle 4

Use a different colour pencil than you did for question 3.1 and colour both angles with the

same colour.

Part 2

3.3 The pairs of equal angles found in questions 3.1 and 3.2 have a special

name.

We call them alternate __3.3.1______ angles.

DAY 3: Activity 4:

Use tissue paper and colour pencils to discover corresponding angles when a transversal cuts

two parallel lines.

Instructions:

On the picture below, using any colour pencil or highlighter, highlight 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝑙.

To answer the questions below slide the tissue paper along 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝑙 to find

matching angles.

Focusing on the angles located at the left side of 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝑙.

Place the tissue paper on top of the picture

4.1 Trace angle 1

4.1.1 Find the angle equal to angle 1.

Colour both angles with the same colour.

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4.2 Trace angle 3

4.2.1 Find the angle equal to angle 3

Use a different colour pencil and colour both angles with the

same colour.

Focusing only on angles located at the right side of 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝑙,

Place the tissue paper on top of the picture above.

4.3 Trace angle 2

4.3.1 Find the angle equal to angle 2

Use a different colour pencil and colour both angles with the

same colour.

4.4 Trace angle 4

4.4.1 Find the angle equal to angle 4

Use a different colour pencil and colour both angles with the

same.

The pairs of equal angles found in questions 4.1, 4.2, 4.3 and 4.4 have

a special name. We call them corresponding angles.

HOMEWORK/CONSOLIDATION

Do the following exercises. The solutions can be found at the end of the lesson.

FIRST ATTEMPT TO DO THE EXERCISE BEFORE YOU WORK THROUGH THE

SOLUTIONS Activity 5

Fill in the missing words and correctly place an angle number / angle pair(s) in the correct box.

Angle numbers may repeat.

Name Angles Transversal EF intersects parallel lines

AB and CD

Interior Angles

Alternate Interior

Angles are ______

Corresponding

Angles are ______

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Vertical

Angles are ______

Activity 6

Calculate the unknown angles and provide a geometric reason for each statement.

6.1

Redding lane and Creek Road are

parallel streets that intersects Park Road

along the west side of Wendell Park.

If ∠1 = 1180, then what is ∠2?

6.3

Find the value of 𝑥.

6.2

Find the value of 𝑥.

6.4

The painted lines that separate parking

spaces are parallel.

The size of ∠1 = 600.

What is the size of ∠2?

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Grade 9 GEOMETRY OF STRAIGHT LINES:

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MEMORANDUM: DAY 2 & 3:

Warm Up

1.Parallel lines are two lines that are always the same distance apart and never intersects. 2.A transversal is a line that intersects two lines at two different points.

3.When a transversal cut a set of lines, 8 angles are formed.

Activity 3

Part 1

3.1.1 Angle 6

3.2.1 Angle 5

Part

3.3 Alternate interior angles

Activity 4

4.1.1 Angle 5

4.2.1 Angle 7

4.3.1 Angle 6

4.4.1 Angle 8

Activity 5

Name Angles Transversal EF intersects parallel lines

AB and CD

Interior Angles

∠3; ∠4; ∠5; ∠ 6

Alternate Interior

Angles are equal

∠3 and ∠6; ∠4 and ∠5

Corresponding

Angles are equal

∠1 and∠5; ∠2 and ∠6; ∠3 and ∠7; ∠4 and ∠8

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Vertical

Angles are equal

∠1 and ∠4; ∠2 and∠3; ∠5and∠8; ∠6and∠7

Activity 6

6.1

Statement Reason ∠1 = ∠2

∴ ∠2 = 1180

(𝐴𝑙𝑡 ∠𝑠, ‖𝑙𝑖𝑛𝑒𝑠)

6.2

Statement Reason

𝑥 = 640 (𝐴𝑙𝑡 ∠𝑠, ‖𝑙𝑖𝑛𝑒𝑠)

6.3

Statement Reason

𝑥 = 1300 ( ∠𝑠 𝑜𝑛 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑙𝑖𝑛𝑒 ; 𝐴𝑙𝑡 ∠𝑠; 𝐶𝑜𝑟𝑟 ∠𝑠 )

6.4

Statement Reason

∠1 = ∠2 ∴ ∠2 = 600

(𝐶𝑜𝑟𝑟. ∠𝑠, ‖ 𝑙𝑖𝑛𝑒𝑠)

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DAY 4: ACTIVITY 7 & 8: LESSON PRESENTATION/DEVELOPMENT

Work through the following activity:

Co-interior angles

The angles 𝐴𝐺𝐻 and 𝐶��𝐺 in the figure are called co-interior angles. They are on the same side

of the transversal.

Consider the figure below and answer the questions that follow.

7.1 What do you know about 𝐶��𝐺 + 𝐷��𝐺? Explain.

7.2 What do you know about 𝐵𝐺𝐻 + 𝐴𝐺𝐻? Explain.

7.3 What do you know about 𝐵𝐺𝐻 + 𝐶��𝐺? Explain.

7.4 What conclusion can you draw about 𝐴𝐺𝐻 + 𝐶��𝐺?

Give detailed reasons for your conclusion.

7.5 When two parallel lines are cut by a transversal, the

sum of two ____7.5.1____angles is ____7.5.2___.

7.6 Another way of saying this is to say that the two

co-interior angles are ___7.6.1___

The prefix ‘co- ‘means together. The word ‘co -interior’ means on the

same side.

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CONSOLIDATION/CONCLUSION

THE FOLLOWING FACTS ARE EXTREMELY IMPORTANT.

Summary of the theorems of parallel lines:

F U n

Corresponding angles

Corresponding angles lie either both above or both below the parallel lines and on the same

side as the transversal. They are the angles in matching corners and are equal. Always look out for the F shape.

Co- interior angles

Co-interior angles lie on the same side of the transversal between the parallel lines. These angles

are supplementary. Always look out for the U shape.

● + ◊ = 180

Alternate angles

Alternate angles lie on opposite sides of the transversal and between the parallel lines.

They are equal in size. Always look out for the Z or N shape.

Corresponding angles Co-interior angles Alternate angles

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HOMEWORK/CONSOLIDATION:

Activity 8

Corresponding angles

If a transversal cuts through two parallel lines, then the pairs of corresponding angles are

equal.

If DB//EC and ABC is a transversal,

then 1ˆB C corr. 's DB//EC

In each of the following calculate the angles marked with x, y and z. Give reasons in

each case.

8.1

8.2

8.3

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Alternate angles

If a transversal cut through two parallel lines, then the pairs of alternate angles are equal.

If AB//CD and BC is a transversal, then ˆB C (alt. 's AB//CD )

Reason: alt. ’s AB//CD

In each of the following calculate, with reasons, the angles marked by small letters.

8.4

8.5

8.6

Co-interior angles

If a transversal cut through two parallel lines, then the pairs of co-interior angles are supplementary i.e.

add up to 180

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Reason: co-int. ’s PQ//TR

In each of the following calculate, with reasons, the angles marked by small letters.

8.7

8.8

8.9

MEMORANDUM: DAY 4:

Activity 7

7.1 They are supplementary (their sum = 180°) because CD is a straight line.

7.2 They are supplementary (their sum = 180°) because AB is a straight line.

7.3 They are alternate angles and they are equal, because AB‖CD

7.4 They are also supplementary (their sum = 180°).

This is because we have already shown that:

C��G is equal to B𝐺H (alt. ∠s AB‖CD)

B𝐺H is supplementary to AGH (∠s on a str. line).

7.5.1 Co-interior angles

7.5.2 180°.

If PQ//TR and RQ is a transversal, then ˆ ˆQ R 180 (co-int. ’s PQ//TR)

T

P

Q

R

R

R

Q

Q T

T

P

P

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7.6.1 supplementary

Activity 8

8.1

𝑥 = 1020 (𝑐𝑜𝑟𝑟. ∠𝑠, 𝑃𝑄‖𝑅𝑆)

8.2

𝑥 = 650 (𝑐𝑜𝑟𝑟. ∠𝑠, 𝐸𝐹‖𝐷𝐺) 𝑦 = 650(𝑐𝑜𝑟𝑟. ∠𝑠, 𝐵𝐴‖𝐷𝐴)

8.3

𝑥 = 720 ( 𝑣𝑒𝑟𝑡. 𝑜𝑝𝑝 ∠𝑠)

𝑦 = 720((𝑐𝑜𝑟𝑟. ∠𝑠, 𝑅𝑄‖𝑇𝑁) 𝑧 = 1080 ( ∠𝑠 𝑜𝑛 𝑠𝑡𝑟. 𝑙𝑖𝑛𝑒)

8.4

𝑎 = 1020(𝐴𝑙𝑡 ∠𝑠. , 𝑃𝑄‖𝑅𝑆)

8.5

𝑥 = 1300 (𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛)

𝑦 = 1300(𝐴𝑙𝑡 ∠𝑠, ‖𝑙𝑖𝑛𝑒𝑠)

8.6

𝑥 = 360( 𝐴𝑙𝑡 ∠𝑠, 𝐷𝐴 ‖𝐸𝐵) 𝑦 = 310( 𝐴𝑙𝑡 ∠𝑠, 𝐴𝐵‖𝐷𝐶) 𝑧 = 670(𝑐𝑜𝑟𝑟. ∠𝑠 𝐴𝐵‖𝐷𝐶)

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8.7

𝑎 = 350(𝑐𝑜 − 𝑖𝑛𝑡 ∠𝑠, 𝐿𝐾‖𝑁𝑀)

𝑏 = 350( 𝑣𝑒𝑟𝑡 𝑜𝑝𝑝 ∠𝑠)

8.8

𝒙 = 𝟏𝟑𝟎𝟎(𝒄𝒐𝒓𝒓. ∠𝒔, 𝑫𝑩‖𝑬𝑭)

𝒚 = 𝟓𝟎𝟎(𝒄𝒐 − 𝒊𝒏𝒕 ∠𝒔, 𝑨𝑩‖𝑪𝑫)

𝟖. 𝟗 4𝑥 + 2𝑥 = 1800(𝑐𝑜 − 𝑖𝑛𝑡∠𝑠, 𝑄𝑃‖𝑆𝑅)

6𝑥 = 1800 ∴ 𝑥 = 300

DAY 5: ACTIVITY 9: LESSON PRESENTATION/DEVELOPMENT

Warm Up activity: Do the 2 exercise in your workbook

Solve the unknown:

1. 4𝑎 − 6 = 34

2. 9𝑚 − 24 = 1 + 4𝑚

Activity 9: Work through the example

9.1 In this diagram AB ∥ CD, EF is a transversal. Calculate the size of HGD.

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CONSOLIDATION/CONCLUSION

NOTE THE FOLLOWING IMPORTANT FACTS. YOU WILL BE REQUIRED TO APPLY THE

FACTS

When solving problems use what you know about the angles between

parallel lines cut by transversal to decide whether lines are parallel or not.

It is important to state in your reason that the lines are parallel. These alternate and

corresponding angles are equal and co-interior angles are supplementary ONLY if lines

are parallel.

The sum of the angles on a straight line is 180°.

When the sum of angles is 180°, the angles are supplementary.

When two straight lines intersect, the vertically opposite angles are equal.

When two parallel lines are cut by a transversal, corresponding angles are equal.

When parallel lines are cut by a transversal, alternate angles are equal.

When two parallel lines are cut by a transversal, the sum of two co-interior angles is 180°.

i.e. co-interior angles are supplementary.

HOMEWORK: Do the exercises

Activity 9

9.2 Determine the value of 𝑥 and 𝑦 in the following diagram:

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MEMORANDUM: DAY 5:

Warm Up:

1. 𝒂 = 𝟏𝟎

2. 𝒎 = 𝟓

Activity 9

9.1

Statement Reason

𝑨��𝑭 = 𝑬��𝑩

∴ 𝑬��𝑩 = 𝟐𝒙 + 𝟏𝟓

𝑯��𝑫 + 𝑬��𝑩 = 𝟏𝟖𝟎𝟎

∴ 𝒙 + 𝟑𝟎𝟎 + 𝟐𝒙 + 𝟏𝟓𝟎 = 𝟏𝟖𝟎𝟎

∴ 𝟑𝒙 = 𝟏𝟑𝟓𝟎

∴ 𝒙 = 𝟒𝟓𝟎

𝑯��𝑫 = 𝒙 + 𝟑𝟎𝟎

𝑯��𝑫 = 𝟒𝟓𝟎 + 𝟑𝟎𝟎

𝑯��𝑫 = 𝟕𝟓𝟎

(𝒗𝒆𝒓𝒕. 𝒐𝒑𝒑 ∠𝒔)

(𝒄𝒐 − 𝒊𝒏𝒕∠𝒔, 𝑫𝑪‖𝑩𝑨)

9.2

Statement Reason

𝒙: 𝟑𝒙 + 𝟏𝟎𝟎 = 𝟒𝟎𝟎

∴ 𝒙 = 𝟏𝟎𝟎

𝒚:

𝟒𝒚 = 𝟑𝒚 + 𝟐𝟎𝟎

∴ 𝒚 = 𝟐𝟎𝟎

(𝒄𝒐𝒓𝒓. ∠𝒔, 𝑻𝑸‖𝑺𝑷)

(𝒂𝒍𝒕 ∠𝒔, 𝑻𝑸‖𝑺𝑷)