Lesson 8B: Angles in a triangle
Yr 8 Objective: understand the proof that the sum of angles of a triangle is 1800
Pre-requisite Learning: Parallel and Perpendicular lines; sum of angles at a point, on a straight
line and in a triangle; vertically opposite angles, corresponding and
alternate angles
Resources: OHP and OHT 8B.1 & 8B.2, whiteboards (ideal but plain paper will do), tracing paper
Vocabulary: Parallel, perpendicular, transversal, acute, obtuse, translate, rotate, corresponding
and alternate angles.
Starter: Using whiteboards, draw two parallel lines with a transversal. Mark two acute, alternate
angles, then mark two obtuse corresponding angles  OHT 8B.1
The highlight the angles on a straight line – put a ruler on the OHT to show that they are
sitting on a straight line.
Main Activity:
In exercise book – draw horizontal parallel lines and mark in the conventional way that
they are parallel (arrows).
On tracing paper trace the parallel lines; set aside for later. In exercise book draw a
transverse line from top right to bottom left and label a pair of acute alternate angles -use
A and a. On tracing paper (away from book) draw a transverse line from top left to bottom
right and label pair of acute corresponding angles above the line – use C and c. Put the
tracing paper on the book so that the tracing extends the parallel lines. Slide the tracing
paper to the left along the parallel lines. What shapes do you make?
Make a triangle so that the base is along the lower parallel line and the apex is on the
upper parallel line. (Watch out – check this is OK for all). Both bottom angles should
already have been labelled. Label third angle in the triangle ‘z’. You should have three
marked angles on a straight line. What fact do we know? (Angles on a straight line) So
what does that tell us? Together write a proof.
Angles on a straight line give A+C+z=180
Since A=a and C=c then we have that a+c+z=180
So angles in a triangle add up to 180.
Plenary:
Using OHT 8B.2 show that the angles in this triangle add up to 180o, using the facts we
know about alternate angles and angles on a straight line.
Additional ideas
Develop this lesson to consider angle sum of quadrilaterals and beyond.
Use resource 8B (or similar) printed on coloured paper. Cut out pairs of triangles – they
share a common length side. On each triangle mark the angles. Agree that the angle
sum is 180o. Put the equal length sides together. What shape is formed? What is the
angle sum for the new shape?
Is it possible to put two triangles together and not get a quadrilateral? What can you get?
What conditions do you need?
Buckinghamshire KS3 Developing Geometrical Reasoning