A point is a dot or cross on a diagram that can be labelled. Points can be connected by either straight or curved lines, and linked together to form shapes
Lines and points form shapes. Shapes can have any number of points and lines.
2-Dimensional shapes exist in two dimensions – width and height.
Shapes can have reflectional or rotational symmetries
Reflectional symmetry is easy to see because one side of a shape is the same (or a reflection of) the other half
A shape with rotational symmetry will still look the same after it has been rotated (turned around a point) by less than one full turn
Types of angle
A) Acute
B) Obtuse
C) Reflex
Interior angles are on the inside of the shape at the vertex
Exterior angles are measured outside of the shape from the extension of one side to the next side.
Perpendicular lines meet at a 90 degree angle
A perpendicular bisector is a line that cuts another line exactly halfway through it. It bisects the line at a right angle.
Bisecting an angle involves constructing a line that cuts an angle exactly in half
A locus (loci plural) is a set of points that follows a certain location rule, for example, always being 3 m away from a point.
The angles around a point add up to 360 degrees
The angles on a straight line add up to 180 degrees
Corresponding angles are equal. They are on the same side of the transversal line and the lines on which the angles lie on form an ‘F’ shape.
Alternate angles are equal. They are on opposite sides of the transversal line and the lines on which they lie form a ‘Z’ shape
Vertically opposite angles are also equal.
Equilateral triangle:
All sides are equal length
All angles are 60 degrees
Isosceles triangle:
2 sides are equal in length
2 angles are equal in size
Scalene triangle:
No sides are equal in length
No angles are equal in size
Square:
2 pairs of parallel sides
4 equal side lengths
4 equal angles of 90 degrees
Rectangle:
2 pairs of parallel sides
2 pairs of equal side lengths
4 equal angles of 90 degrees
Rhombus:
2 pairs of parallel sides
4 equal side lengths
Opposite angles are equal
Trapezium:
1 pair of parallel sides
Isosceles Trapezium:
1 pair of parallel sides
1 pair of opposite sides with equal length
2 pairs of adjacent equal angles
Two shapes are similar if they are the same shape but one may be an enlargement of the other.
Two shapes are congruent if they are exactly the same shape and have the same size.
Translations involves moving the shape in different directions without making any changes to the size of the original shape.
Centre of rotation: The fixed point around which the shape is turned.
The centre of the circle is the point that is at an equal distance from all the points on the circumference of the circle
The radius is a line that joins the centre of the circle with a point on the circumference.
The diameter is a line that joins a point on the circumference with another point on the circumference and passes through the centre point.
The circumference is also known as the perimeter of the circle and defines the distance around the outside of the circle
A tangent is a line that touches the circle at only one point. The tangent meets the radius at a perpendicular angle (90°).
An arc is a portion of the circumference of the circle.
A chord is a straight line joining two points on the circumference
A sector of a circle is a portion of a circle and is “pie-shaped”. Its perimeter is made up of two radii and a portion of the circumference (arc).
A segment of a circle is the area enclosed by an arc and a chord of the circle.
Circle theorem 2: Angle at the centre of the circle is twice the angle at the circumference
Circle theorem 1: When a radius meets a tangent, the angle will always be 90 degrees