Part 4: Geometry and measures

    Cards (70)

    • 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