Download Properties of Polygons

Yr 9 Unit 2 – Shape, Space and Measure – Higher
8 lessons
PROPERTIES
OF POLYGONS
Support 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 properties
Unmarked angles worksheet (starter)
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.
3 Use angle properties of isosceles, equilateral and right-angled
triangles.
AQA Foundation pages 54 – 55.
FVT Angle properties
Grade
E
Ref
F3.2c
E
F3.2c
E
F3.2d
Core Objectives
1 Classify a quadrilateral by geometric properties.
Classifying quadrilaterals worksheet
FVT Angle properties
2 Calculate exterior and interior angles of a regular polygon.
Regular polygons worksheet
ET Regular polygons
ET Regular polygons starter
Grade
C
Ref
H3.2c
C
H3.2a
H3.2d
H3.2h
Extension Objectives
Grade
1
2
Vocabulary
Exterior angles
Isosceles triangle
Pentagon
Octagon
Isosceles trapezium
Rhombus
Irregular polygon
Equilateral triangle
Right-angled triangle
Hexagon
Nonagon
Trapezium
Kite
Interior angle
Congruent
Polygon
Heptagon
Decagon
Parallelogram
Square
Convex polygon
Ref
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
Pentagon triangles investigation.
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.
Y9 Angles facts 1
Y9 angles parallel lines
Angles in irregular polygons
Regular polygons
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.