Year 9 Mathematics Booster level 4  5
Lines and Angles
OBJECTIVES


Use correctly the vocabulary, notation and labelling conventions for lines, angles
and shapes (Y7).
Use angle and side properties of parallel and intersecting lines, triangles and
quadrilaterals to solve problems (Y8)
VOCABULARY

Parallel, transversal, intersecting, vertically opposite, supplementary,
complementary, alternate, corresponding, interior, exterior, equidistant
RESOURCES

OHTs, mini white-boards, Shape sorting activity cards, worksheets
ORAL AND MENTAL STARTER
10 Minutes
Q: What angles can we see?
Ask pupils to come to the board to show the following angles:
ABD
BED
CBE
ABC
BED
EDB
Q: Which of these are equivalent to ‘x’
Which equivalent to ‘y’; which equivalent to ‘p’
Which angles are acute, which obtuse.
At this point it might be appropriate to consider estimation of angles and angle
measurement
MAIN TEACHING
40-45 minutes
Angle Facts
A.
B.
C.
D.
E.
F.
Angles on a straight line add up to 180o
Angles around a point add to 360o
Angles in a triangle add up to 180o
The exterior angle of a triangle is equal to the sum of the two interior opposite angles
Vertically opposite angles are equal
Angles in a quadrilateral add up to 3600
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Lines and Angles
Using mini white boards ask pupils to show A,B,D&E (See OHT F1)
Q: If ABD = 115o, BED = 55o
Find BDE describing the
angle facts used
Pupils can then use worksheet
provided
Questions 13
To extend/ consolidate
More angle facts:
G. Alternate angles between parallel lines are equal
H. Corresponding angles between parallel lines are equal
I. Interior angles between parallel lines add up to 180o
Ask pupils to draw a pair of parallel lines and a transversal on white boards and then
illustrate the angle facts (see OHT F2)
Which sides are parallel – why? (due to notation)
If ABG = xo – which other angles equal x? – Give reasons.
Consolidation on work sheet questions 4&5
Introduce “Shape sorting by angles” card sorting activity - Pupils can then work through
rest of sheet.
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Lines and Angles
PLENARY
5 - 10 minutes
See OHT F3
BCGF is a parallelogram. ABF = 1320
Q: What extra information is that giving us? Annotate the diagram
Q: Which other angles equal 1320 – and why?
What do the other angles equal?
Now draw line DG and extend to cross BF produced at J
Q: What shapes can you now see?
(Look for trapezia, triangles etc insist on correct labelling)
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Lines and Angles
Worksheet F1 – lines and angles
In the questions following you will need to refer to the following angle facts and quote which
are used each time:
Angle Facts:
1
Angles on a straight line add up to
1800
5
Vertically opposite angles are equal
2
Angles around a point add up to 3600
6
Angles in a quadrilateral add up to 3600
3
Angles in a triangle add up to 1800
7
Alternate angles between parallel lines
are equal
4
The exterior angle of a triangle is
equal to the sum of the two interior
opposite angles
8
Corresponding angles between parallel
lines are equal
9
Interior angles between parallel lines add
up to 1800
Q1: Find angle p. Using the angles to give reasons for your answer
Q2: Find angles q, r and s. Explain how you found each one, referring to the list of angle
facts
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Lines and Angles
Q3: Work out the size of angles t, u and v. Use the angle facts to explain how you reached
your answer
Q4: Find angles x, y and z. For each one, give the angle fact used to calculate the answer
Q5: a) Which angle is equal to p? State the appropriate angle fact
Q5: b) Calculate the size of p, q, r and s. Recording the angle facts used
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Lines and Angles
Q6: Find angles x, y and z. For each one give the angle fact used to calculate the answer
Q7a: What quadrilateral is outlined in this diagram?
Q7b: Find angles s, t, u and v
Q8: ABCD is a parallelogram. Find each of the lettered angles giving reasons for each
calculation made
Q9a: What quadrilateral appears in this diagram?
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Q9b: Work out angles m, n and p.
Q9c: What can you say about triangle BCI?
Buckinghamshire Secondary Mathematics Curriculum Resources
Lines and Angles
Year 9 Mathematics Booster level 4  5
Lines and Angles
Resource F-1
Shape Sorting Activity by angle properties
I have 3 equal
angles
I have 3 angles
only two of them
are equal
I have a right
angle and two
angles of 45o
I have 3 angles
none of them
are equal.
I have 3 angles,
none of them
are equal but I
do have a right
angle
I have 4 angles
including one
reflex angle
Equilateral
triangle
I have 4 right angles
and all my sides are
the same length
Isosceles
triangle
I have 2 pairs of
opposite and equal
angles, but all my
sides are the same
length
Right-angled
Isosceles triangle
I have 4 right angles
and two pairs of
opposite, equal and
parallel sides
Scalene
Triangle
Right–angled
Triangle
Delta or
Arrow head
Opposite sides are
equal and parallel,
opposite angles are
equal, but with no
right angles
Square
Rhombus
Rectangle
Parallelogram
I have 4 sides, one
pair of opposite sides
is parallel
Trapezium
I have 4 angles, one
pair of opposite
angles are equal
Kite
Buckinghamshire Secondary Mathematics Curriculum Resources