Right Angle Triangle. Square. Opposite sides are parallel
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1 Triangles 3 sides ngles add up to 18⁰ Right ngle Triangle Equilateral Triangle ll sides are the same length ll angles are 6⁰ Scalene Triangle ll sides are different lengths ll angles are different Isosceles Triangle 2 sides are the same 2 angles are the same Quadrilaterals 4 sides ngles add up to 36⁰ Rectangle Opposite sides are the same length Opposite sides are parallel ll angles are 9⁰ Square ll sides are the same length Opposite sides are parallel ll angles are 9⁰ Rhombus ( Wonky square ) ll sides are the same length Opposite sides are parallel Opposite angles are equal Parallelogram ( Wonky Rectangle ) Opposite sides are the same length Opposite sides are parallel Opposite angles are equal Kite Two sides are the same length and next to each other The other two sides are also the same length and next to each other Trapezium Two sides parallel but have different lengths Regular Shapes ll sides are the same length ll angles are the same Equilateral Triangle Square Pentagon Hexagon Heptagon Octagon Decagon 3D Shapes Vertices corners Edges Faces sides Cube Cuboid Cylinder Triangular Prism Triangular ased Pyramid Sphere
2 ngles nti-clockwise 36⁰ ⁰ Clockwise 2 nd Quadrant 1 st Quadrant cute ngles between ⁰ and 9⁰ 27⁰ Reflex ngles between 18⁰ and 36⁰ 9⁰ Obtuse ngles between 9⁰ and 18⁰ Circle 36⁰ 3 rd Quadrant 4 th Quadrant 18⁰ Straight Line 18⁰ Special Words and Symbols Perpendicular Two lines that are at right angles to each other Right-angle 9⁰ Vertical Straight up Perpendicular to horizontal Parallel Two lines that are always the same distance apart One or two arrows are used to show that the lines are parallel When Lines are the Same Length small line is used to show that the lines are the same length Horizontal Straight across Parallel to level ground or say the bottom of a page
3 ngle Facts Opposite ngles When two straight lines cross Corresponding ngles opposite angles are equal corresponding angles are equal lternate ngles Interior ngles alternate angles are equal interior angles add up to 18⁰ Examples Find angles a and b ngles in a triangle add up to 18⁰ so, a + 44⁰ + 72⁰ = 18⁰ a = 64⁰ 72⁰ b Interior ngles add up to 18⁰ so, a + b = 18⁰ 44⁰ a b = 116⁰ Find angles a, b, c, d and e c d e b ngles on a straight line add up to 18⁰ so, a + 112⁰ = 18⁰ a = 68⁰ a and b are Corresponding ngles so, b = 68⁰ a 112⁰ b and c are Opposite ngles so, c = 68⁰ c and e are Corresponding ngles so, e = 68⁰ ngles on a straight line add up to 18⁰ so, d + e = 18⁰ a = 112⁰
4 Reflective Symmetry Fold a sheet of paper in half. Unfold. Paint half a butterfly on the left side of the paper. Fold the paper in half. Unfold. There is now a reflection of the painting on the right side. The fold is called the mirror line. It may be helpful to use a mirror and tracing paper. mirror line reflected When the mirror line is on a diagonal, it may help to turn the paper first. Lines of Symmetry Equilateral Triangle (3) Various shapes are shown below with their lines of symmetry. The number is how many lines of symmetry that shape has. Isosceles Triangle (1) Square (4) Rectangle (2) Parallelogram () Trapezium (1) Pentagon (5) Hexagon (6)
5 Rotational Symmetry The shapes below are rotated about a point. This point is called the centre of rotation. 1 up 2 right 1 right 2 up Rotated 9⁰ anti-clockwise. Check Rotated 18⁰ clockwise. Check 2 right 2 up 2 left 2 down Tip Rotate 9⁰ clockwise about the point Try tracing the shape. Leave the tracing in place. Put your pencil on the tracing paper over the centre of rotation and make a small hole. Hold the pencil still. Rotate the tracing paper 9⁰ clockwise (a quarter turn) Use the tracing to draw the shape in its new position. Check.
6 Translations translation is where a shape slides into a different position. The shape remains the same. Here the shape has been translated from point to point. Each vertices, (corner), of the shape moves exactly 5 squares right. If this didn t happen then the shape would change. Here the shape has been translated from point to point. Each corner of the shape moves exactly 3 squares right and 2 squares up. Here the shape has been translated from point to point. Each vertices of the shape moves exactly 5 squares down and 5 squares left.
7 Nets net is what a 3D shape looks like when it is unfolded. Look at this cube as it unfolds. This is the net of this cube. There are many ways to unfold a cube, resulting in different nets. How many can you find? Here are some more 3D shapes and nets.
8 Scale Factors Shapes can be enlarged or shrunk by a scale factor. If the scale factor is 2 then the new shape will be double the size of the original shape. The shape will change about a given point. Scale Factor of 2 Scale Factor of 3 C C This triangle will be enlarged by a scale factor of 3 about the origin. Draw lines from the origin through each vertex. ' ' C' C C has coordinates (1, 1) so ' will be at (3, 3) has coordinates (1, 2) so ' will be at (3, 6) C has coordinates (3 1,1) so C' will be at (1, 3) 3 Draw the enlarged triangle
9 Examples Scale factor of 4 about. Scale factor of 2 about. Scale factor of 3 about the origin. Translated to then enlarged by a scale factor of 2 Rotated 18⁰ clockwise about then enlarged by a scale factor of 4 Rotated 9⁰ clockwise about then enlarged by a scale factor of 3
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