Page 1 of 20 Grade 9 GEOMETRY OF STRAIGHT LINES: (Draft) 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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Page 1 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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
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:
Page 4 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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
Page 5 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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
Page 6 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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.
Page 7 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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.
Page 8 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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 ______
Page 9 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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?
Page 10 of 20
Grade 9 GEOMETRY OF STRAIGHT LINES:
(Draft)
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