Lesson 9A
Finding angles and justifying
Y9 Objective: Solve problems using properties of angles, of parallel and intersecting lines,
and of triangles and other polygons, justifying inferences and explaining reasoning with
diagrams and text;
Pre-requisite learning:
Y7 objectives:
Identify parallel and perpendicular lines; know the sum of angles at a
point, on a straight line and in a triangle, and recognise vertically opposite angles. Begin to
identify and use angle, side and symmetry properties of triangles and quadrilaterals; solve
geometrical problems involving these properties, using step-by-step deduction and explaining
reasoning with diagrams and text.
Y8 objectives:
Identify alternate angles and corresponding angles; understand a proof
that: the sum of the angles of a triangle is 180o
and of a quadrilateral is 360o ; Solve
geometrical problems using side and angle properties of equilateral, isosceles and right-angled
triangles and special quadrilaterals, explaining reasoning with diagrams and text.
Resources needed: OHP plus OHTs 9A.1 and 9A.2, whiteboards, angle fact cards, worksheet 9A
Vocabulary: alternate and corresponding angles, parallel lines, transversal, justify, generalise.
Starter:
Whiteboards
(Visualisation: you may wish to ask pupils to shut their eyes)
Imagine a pair of parallel lines.
Now add a transversal (non-perpendicular) to your pair of parallel lines.
How many differently sized angles can you see?
Draw ‘your picture’ on your whiteboard and mark the equal angles.
Show me.
Mark with the letter ‘a’ a pair of alternate angles.
Show me.
Mark with the letter ‘b’ a different pair of alternate angles.
Show me
Mark with the letter ‘c’ a pair of corresponding angles.
Look at my OHT (9A.1). Which two lines are parallel?
Show me
Write down an angle equal to  JBA (select different answers and ask students to justify their
response)
Write down an angle equal to  BCG. (ditto)
{What quadrilateral is enclosed?.
Rotate the line KL about point G until it is parallel to JI; what quadrilateral is now enclosed?}
Main activity:
Angle fact cards
OHT 9A.2 if  PBC = 43o, find  CAB.
Model how to find other angles and record stages. Ask pupils to guide you through the stages.
‘If we know  PBC = 43o, what other information can we deduce?’ Stick relevant angle fact card
on the board when mentioned.
Hand out worksheet, pupils to work in pairs and then convince another pair sat near them. (You
may wish to allocate these groupings carefully)
‘red’ pairs work on questions 1, 3, 5, 7
‘green’ pairs work on questions 2, 4, 6, 8
(You may wish to hand out A3 paper so each group of 4 produces one perfect solution for the
plenary)
Plenary:
OHT 9A.2
Call unknown angle ( PBC) = x. and find  CAB
Have a ‘scribe’ recording steps with x, class use whiteboards to respond to steps led by teacher.
What can you tell me about  PBC and  CAB; is this always true? How do you know?
{It may be useful to record this on a large sheet of flipchart paper as it could then be used in the
lesson 9B}
{lower sets, reinforce by giving numerical values e.g. so if PCB is 50, what is CAB}
Buckinghamshire KS3 Developing Geometrical Reasoning