Details of Class: Lesson 5
Date:
Time: 100mins
Learning Intentions/Topic:
Year: 8
Geometry: Angles and Parallel lines
Recognise parallel lines and calculate angles
made by parallel lines and a transversal.
Know and recognise the different types of
angles that can be made by the transversal.
Terms to know:
Parallel
Transversal
Intersect
Vertically Opposite Angles
Corresponding Angles
Co-Interior Angles
Alternate Angles
Resources Required:
Room:
No. of students:
Relationship to VELS:
Use angle relations involving transversals and
pairs of parallel lines to solve problems, giving a
reason for the solution
Using language relevant to the topic
Students to each have their own workbook and stationery
Maths Quest 8 textbook
Worksheets and Examples (provided)
Whiteboard & Markers
Ruler
Introduction/Housekeeping/Warm-up:
Link to last lesson : Previously we looked at calculating angles in triangles, quadrilaterals and other
polygons. Now we will investigate different angles associated with parallel lines.
2 min
Content
Description:
What are parallel lines?
Parallel lines are lines that never meet.
A line that intersects (crosses over) a pair (or set) of parallel
lines is called a transversal.
Draw this on the board labelling what are the parallel lines and
what is the transversal.
There are many angles that are made when a transversal
crosses a set of parallel lines. Let’s look at the different types of
angles that are made.
Read through description as a class of the four different angles
(p. 264 of Maths Quest 8) that are made when a transversal
crosses parallel lines.
- Vertically Opposite angles (X shape)
- Corresponding angles (F shape)
- Co-interior angles (C shape)
- Alternate angles (Z shape)
Activity: With the help of the information on p. 264, students
are to complete the table provided.
Resources
Time
10 min
Whiteboard &
Markers, Ruler
Maths Quest 8 p.264
Angles and Parallel
lines table provided
7 min
Quickly go through the answers to the table. Answer any
questions that arise.
2 min
Examples on board of how to find angles made by transversal
and parallel lines. See sheet of examples provided.
Example sheet
10 min
Activity: Students to complete Ex 7G p.267 questions 2 - 14
Maths Quest 8 p.267
Remainder
of Lesson
Activity: When/if students finish Ex 7G, students are to
complete:
- Summary questions (fill in the blank) provided
- Chapter review questions 1- 14 p. 287 – 289
Summary questions
Maths Quest 8
pp.287 - 289
Reinforcement of Ideas/Questioning/Homework:
Questions?
Homework: Finish any unfinished questions from today’s activities.
Overall reflection of lesson:
3 min
Angles and Parallel lines
Complete the table below. Keep completed table for your own reference.
Diagram
Type of angle relation
Associated shape
Rule
X
Corresponding
Alternate
Are equal in size
Z
Add up to 180°.
Angles and Parallel lines
Answers:
Diagram
Type of angle relation
Associated shape
Rule
Vertically Opposite
X
Are equal
Corresponding
F
Are equal in size
Alternate
Z
Are equal
Co-interior
C
Add up to 180°
Examples:
1. For the diagram provided:
a) State the type of angle relationship
b) Find the value of the pronumeral
115˚
m
a) The angles shown are co-interior
b) m + 115˚ = 180˚
m = 180˚ – 115˚
m = 65˚
2. Find the value of the pronumeral in the diagram shown.
85˚
x
85˚
y
x
y = 85˚ (as corresponding angles)
x + y = 180˚ (as supplementary angles)
x + 85˚ = 180˚
x = 180˚ - 85˚
= 95˚
Summary
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An _____________ triangle has all 3 sides of equal length and all 3 angles equal.
An isosceles triangle has _______________ of equal length and 2 base angles equal.
All sides and all angles are different in ____________ triangles.
An acute-angled triangle has all angles _________________ 90˚.
An obtuse angled triangle contains one _____________angle.
A ______________________triangle contains one 90˚ angle.
The sum of the _______________ angles in any triangle is 180˚.
An ________________________ of a triangle is equal to the sum of the two interior angles,
not adjacent to it.
All _________________________can be divided into 2 groups: parallelograms and others.
Parallelograms have 2 pairs of_______________________ and include rectangles, squares,
parallelograms and rhombi.
A rectangle has two pairs of opposites sides equal and all four angles are ________ angles.
A ______________has all 4 sides of equal length and four right-angles.
A parallelogram has two pairs of ________________________ of equal length and opposite
angles of equal size.
A rhombus has __________________ sides of equal length and opposite angles of equal size.
Other quadrilaterals include kites, _________________ and irregular quadrilaterals.
The _______________________ of a kite are equal in length and the angles between the
unequal sides are equal in size.
A trapezium is a quadrilateral with _________________ of parallel sides.
An _________________ quadrilateral does not have any special features.
The sum of the interior angles in any quadrilateral is ___________.
The sum of the interior angles is any polygon = 180˚ × (n – 2), where n is the
_______________________ in the polygon.
A _____________ polygon has all sides of equal length and all angles of equal size.
A ______________is a line that intersects a pair (or set) of parallel lines.
Corresponding angles (F-Shaped), ______________ angles (Z-shaped) and
____________________________ angles (X-shaped) are equal in size.
Co-interior angles are _____________________ (that is, add to 180˚).
Word List:
360˚
adjacent sides
all four
alternate
equilateral
exterior angle
interior
irregular
number of
sides
obtuse
one pair
opposite sides
parallel sides
quadrilaterals
regular
right
right-angled
scalene
smaller than
square
supplementary
transversal
trapeziums
two sides
verticallyopposite
Summary | Answers
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An equilateral triangle has all 3 sides of equal length and all 3 angles equal.
An isosceles triangle has two sides of equal length and 2 base angles equal.
All sides and all angles are different in scalene triangles.
An acute-angled triangle has all angles smaller than 90˚.
An obtuse angled triangle contains one obtuse angle.
A right-angled triangle contains one 90˚ angle.
The sum of the interior angles in any triangle is 180˚.
An exterior angle of a triangle is equal to the sum of the two interior angles, not adjacent to
it.
All quadrilaterals can be divided into 2 groups: parallelograms and others.
Parallelograms have 2 pairs of parallel sides and include rectangles, squares, parallelograms
and rhombi.
A rectangle has two pairs of opposite sides equal and all four angles are right angles.
A square has all 4 sides of equal length and four right-angles.
A parallelogram has two pairs of opposite sides of equal length and opposite angles of equal
size.
A rhombus has all four sides of equal length and opposite angles of equal size.
Other quadrilaterals include kites, trapeziums and irregular quadrilaterals.
The adjacent sides of a kite are equal in length and the angles between the unequal sides are
equal in size.
A trapezium is a quadrilateral with one pair of parallel sides.
An irregular quadrilateral does not have any special features.
The sum of the interior angles in any quadrilateral is 360˚.
The sum of the interior angles is any polygon = 180˚ × (n – 2), where n is the number of sides
in the polygon.
A regular polygon has all sides of equal length and all angles of equal size.
A transversal is a line that intersects a pair (or set) of parallel lines.
Corresponding angles (F-Shaped), alternate angles (Z-shaped) and vertically opposite angles
(X-shaped) are equal in size.
Co-interior angles are supplementary (that is, add to 180˚).