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Yr 9 Unit 2 – Shape, Space and Measure – Foundation
8 lessons Properties of triangles
Support Objectives
1 Identify isosceles, equilateral and right-angles triangles.
Grade
G
Ref
F3.2d
G
F3.2d
Grade
E
Ref
F3.2c
E
F3.2c
E
F3.2d
Grade
Ref
AQA Foundation I page 53.
Mathsnet.net – identify triangles
Mathsnet.net – identify triangles 2
Mathsnet.net – drawing triangles
Mathsnet.net – drawing triangles 2
2 Use the word ‘congruent’ when triangles are identical.
AQA Foundation I page 54
Mathsnet.net – congruent triangles 1
Core Objectives
1 Show that the angles of a triangle add up to 180 degrees and use
this to find angles.
AQA Foundation I pages 49 - 50.
FVT Angle Facts
Mathsnet.net – show angles add up to 180
Mathsnet.net – measure angles in a triangle
Mathsnet.net – proof using alternate angles
Waldomaths.com – angles in a traingle
2 Show that an exterior angle of a triangle is equal to the sum of the
interior opposite angles.
AQA Foundation I pages 51 – 52.
Waldomaths.com – exterior and interior angles of a triangle
3 Use angle properties of isosceles, equilateral and right-angled
triangles.
AQA Foundation pages 54 – 55.
FVT Angle Facts
Mathsnet.net – angles in isosceles triangles
Extension Objectives
1
Vocabulary
Exterior angles
Isosceles triangle
Equilateral triangle
Right-angled triangle
Congruent
Ideas for starters
*Each student draws and cuts out a triangle, tears off the corners and arranges as angles on a straight
line (triangles could be prepared for them).
*Each student draws any triangle, measures the angles and finds the total. (Students could work in
pairs.) Discuss accuracy and the difference between examples and a formal proof.
*Use a dynamic geometry software package to draw a triangle and display its angles. Change the shape
of the triangle and ask students to find the angle sum after each change.
*Demonstrate how to draw a set of exterior angles for a triangle. Each student draws a triangle and set
of exterior angles, then measures all the angles and looks for relationships between them. (Could work in
pairs or groups.) Discuss accuracy and the difference between examples like these and a formal proof.
* Use a dynamic geometry software package to draw a triangle and one of its exterior angles. Display
the size of each angle, then ask students to calculate the sum of the interior opposite angles as you
change the shape of the triangle.
* Explain how to use compasses and ruler to construct an equilateral triangle. Students each draw an
isosceles triangle (two equal sides) and measure the angles. Discuss congruence and similarity.
*Students cut out equilateral and isosceles triangles and fold them to match equal angles. Discuss
congruence and similarity.
*Use a dynamic geometry package to draw an equilateral triangle and display each of its angles. Show
that the angles do not change as you change the size of the triangle. Repeat with an isosceles triangle
and look at the way its angles change as you change the shape and size of the triangle. Also discuss
congruence and similarity.
HOLS/maths investigations
* AQA Foundation I pages 52, 54.
ICT links / citizenship
Ideas for plenaries
* Display a number of sets of three angles e.g. A=55, B=105, C=20. Ask students to decide which sets
could be the angles of the triangle.
*Display diagrams involving angles and ask students which are incorrect and why.
*Display diagrams involving angles and ask students to use the exterior angle rule to say whether the
given exterior angles are correct or not.
*Display diagrams of different triangles put together and ask the students to count the number of
equilateral, isosceles or right-angled triangles they can see. Alternatively, label the shapes with letters
and ask students to name pairs of congruent triangles and/or pairs of similar triangles.
*Students cut out two congruent scalene triangles and fit them together to form an isosceles triangle
(pairs of triangles could be prepared earlier and laminated for repeat use).
Ideas for homework
* AQA Foundation I Homework book. Chapter 5. Numbers 1, 2, 3.
Ideas for Formative Comments
* Make sure you can identify the different triangles.
* Make sure you can identify congruent triangles even when they are drawn in different positions.
* Remember that the angles in a triangle add up to 1800 and use this to find the size of other angles.
* Learn the angle properties for equilateral, isosceles and right angle triangles.