Types of triangles

Know your triangles Teacher notes Ask the pupils what type of triangle cannot be drawn using this grid. Challenge the pupils to create 8 unique triangles, taking a ‘picture’ of each one. Pupils should be able to describe the triangles they have created using the correct terminology of acute, obtuse, scalene and isosceles.

Angles in a triangle Look at triangle ABC shown below: c Photo credit: © Freddy Eliasson 2010, Shutterstock.com For any triangle, the interior angles will add up to 180 How do we know this? How can we prove that this is true?

Interior angles in a triangle

Exterior angles of a triangle

Interior and exterior angles in a triangle Teacher notes Drag the vertices of the triangle to show that the exterior angle is equal to the sum of the opposite interior angles. Hide angles by clicking on them and ask pupils to calculate their sizes. Be aware that the angles are rounded to the nearest degree and that this may cause a slight error of ±1°.

Calculating angles

Quadrilaterals Quadrilaterals are named according to their properties. A shape can be classified according to whether it has: equal and/or parallel sides equal angles right angles diagonals that bisect each other Teacher notes List the properties that we use to classify shapes. Some of these properties define the shape. These are the minimum requirements needed to define the shape. Other properties, such as symmetry properties, are derived properties and happen as a result of the definition. diagonals that are at right angles lines of symmetry rotational symmetry.

Quadrilaterals Teacher notes Work through each description in turn and pupils to suggest everyday objects exemplifying these shapes. Parallelogram Draw pupils’ attention to the convention of using double dashes to distinguish between the two pairs of equal sides and the use of double arrow heads to distinguish between two pairs of parallel sides. State that when two lines bisect each other, they cut each other into two equal parts. Ask pupils for other derived properties such as the fact that the opposite angles are equal and adjacent angles add up to 180º. Stress, however that a parallelogram has no lines of symmetry. Ask pupils if they know the name of a parallelogram that has four right angles (a rectangle), a parallelogram that has four right angles and four equal sides (a square) and a parallelogram with four equal sides (a rhombus). A parallelogram can be thought of as a slanted rectangle. Rhombus Ask pupils for other derived properties such as the fact that the opposite angles are equal. Ask pupils if they know the name of a rhombus that has four right angles (a square). A rhombus can be thought of as a slanted square. Rectangle Ask pupils for other derived properties such as the fact that the diagonals are of equal length and bisect each other. Ask pupils to explain why it is possible to describe a rectangle as a special type of parallelogram. Arrowhead Ask pupils for other derived properties such as the fact that one pair of angles is equal. Ask pupils if a kite can ever have parallel sides. The answer is no. Square Ask pupils for other derived properties such as the fact that the diagonals are of equal length and bisect each other at right angles. Ask pupils to explain why it is possible to describe a square as a special type of parallelogram, a special type of rhombus or a special type of rectangle. Trapezium A trapezium has one line of symmetry when the pair of non-parallel opposite sides are of equal length. It can never have rotational symmetry. Isosceles trapezium Ask pupils for other derived properties such as the fact that there are two pairs of equal adjacent angles. Kite Ask pupils for other derived properties such as the fact that there is one pair of opposite angles that are equal. Ask pupils if a kite can ever have parallel sides. Conclude that this could only happen if the four sides were of equal length, in which case it would no longer be a kite, but a rhombus.

Know your shapes

Quadrilaterals on a 3 by 3 pegboard Teacher notes Challenge pupils to find the 16 distinct quadrilaterals (not including reflections, rotations and translations) that can be made on a 3 by 3 pegboard. Classify them according to their side, angle and symmetry properties.

Quadrilaterals A tiler is looking at some square and equilateral triangle shaped tiles, each with sides of 20 cm. Using angles, can he check if the equilateral triangles and squares will tessellate together? Teacher notes The square has angles of 90° Each angle in an equilateral triangle is 60° This means that 2 squares and 3 triangles will fit around a point, adding up to 360° 90° + 90° + 60° + 60° + 60° = 360° Investigate other triangles and quadrilaterals that he could use together to make tessellating floor patterns.