Geometry

Worked examples (12)extended set

• 1Angles on a line and at a point
• 2Angles between parallel lines
• 3Exterior angle of a triangle
• 4Isosceles triangle angles
• 5Angles in a quadrilateral
• 6Angles with algebra
• 7A bent line between two parallel lines
• 8Trapezium with an isosceles triangle inside
• 9Show that two lines are parallel, then prove a triangle is isosceles
• 10Two lines crossing a pair of parallel lines
• 11Quadrilateral with extended sides and an isosceles triangle
• 12A line inside a right-angled triangle

Worked examples (12)extended set

• 1Sum of interior angles
• 2Finding the number of sides from an exterior angle
• 3Working back from an interior angle
• 4Missing angle in an irregular polygon
• 5Finding n from the angle sum
• 6Fitting polygons around a point
• 7Exterior angles of an irregular hexagon, in algebra
• 8Diagonals of a regular pentagon
• 9A ring of regular pentagons
• 10Three regular tiles around a point, angles in a ratio
• 11A diagonal of a regular polygon
• 12Naming a quadrilateral from its properties

Worked examples (11)extended set

• 1Finding the hypotenuse
• 2Finding a shorter side
• 3The converse — testing for a right angle
• 4Distance between two coordinates
• 5Isosceles triangle split into two right angles
• 6Pythagoras in three dimensions
• 7Two right-angled triangles sharing a side
• 8A triangle split by its height — is the top angle a right angle?
• 9Shortest route over the surface of a cuboid
• 10Edging a flower bed — the missing sloping side
• 11Total height of a toy rocket

Worked examples (12)extended set

• 1Missing side in similar triangles
• 2Proving two triangles are similar
• 3Area scale factor
• 4Volume scale factor
• 5Working backwards from an area ratio
• 6Scale in context
• 7Parallel line inside a triangle — finding the missing parts
• 8Similar triangles facing different ways, with areas
• 9Water in a cone-shaped container
• 10Similar storage jars — height from capacities
• 11Similar candles — a height from surface areas
• 12Volume of a frustum using similar pyramids

Worked examples (11)extended set

• 1Lines and order of symmetry
• 2Symmetry of regular polygons
• 3Planes of symmetry in three dimensions
• 4Identifying a shape from its symmetry
• 5Rotational symmetry and angle of rotation
• 6Completing a shape to give a required symmetry
• 7Shading squares to give rotational symmetry
• 8Two parallel chords of a circle
• 9Planes and axes of symmetry of a prism and a pyramid
• 10Adding squares to a grid pattern for line symmetry
• 11Planes and axes of symmetry — pyramid and prism

Worked examples (12)extended set

• 1Angle at the centre
• 2Angle in a semicircle
• 3Cyclic quadrilateral
• 4Tangents to a circle
• 5Angles in the same segment
• 6Combining circle theorems
• 7Radii make an isosceles triangle — and spotting a doubling error
• 8Tangent, diameter and a cyclic quadrilateral together
• 9Two tangents with algebra, then a point on the minor arc
• 10Radii, a tangent and a triangle inscribed in a circle
• 11Cyclic quadrilateral with a tangent and parallel sides
• 12Five points on a circle

Worked examples (9)extended set

• 1Measuring a scale drawing to find a real distance
• 2Locating a point from two distances with compasses
• 3Completing a scale drawing of a triangle from three sides
• 4Constructing a rhombus from two triangles
• 5Scale drawing with a bearing
• 6Drawing the net of a prism with equilateral ends
• 7Using measurements from the net of a prism
• 8Interpreting a compass construction on a scale drawing
• 9From the net of a pyramid to its volume