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2d Shapes 2d means the shape only has 2 dimensions - length and height Shapes usually are categorised by the number of sides they have The most common ones are listed Sides 1 2 3 4 5 6 7 8 9 10 11 12 Name Line Does not exist Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Unidecagon Dodecagon If the name finishes in hedron it is a three dimensional shape as in dodecahedron, which is a 12 sided, three dimensional shape The shapes are further categorised because if the edges are all the same length, & the angles are all the same, they are called Regular shapes. If not they are called irregular shapes. This is a regular triangle This is an irregular triangle This is a regular Quadrilateral Page 1 of 9 This is an irregular Quadrilateral This is a regular Pentagon This is an irregular Pentagon Triangles Triangles are given names which reflect their properties A triangle in which all of the angles and sides are of different length is called a scalene triangle A triangle in which has a right angle (90º) in it is called a right angled triangle Page 2 of 9 A triangle with two sides the same length has two angles the same size, is called an isosceles triangle A triangle with three sides the same length has three angles the same size, is called an equilateral triangle A special case is a right angled Isosceles triangle. It has two sides, and two angles, that are the same. The third angle is a right angle Exercise Name the triangles from the word list Page 3 of 9 Quadrilaterals All quadrilaterals have 4 sides A quadrilateral that has opposite sides the same length and all of the corners (Vertices) are 90º (opposite sides are parallel), is called a Rectangle A rectangle that has all 4 sides the same length is called a Square A rectangle that looks like it has been βpushed overβ is called a Parallelogram It has opposite sides and opposite angles the same size A square that looks like it has been βpushed overβ is called a Rhombus It has all four sides and opposite angles the same size A quadrilateral with two pairs of adjacent (next to) sides the same length and two of the opposite angles are the same size, is called a Kite A quadrilateral one pair of parallel sides is called a Trapezium Page 4 of 9 Exercise Name the Quadrilaterals from the word list Page 5 of 9 Congruency & Similarity Page 6 of 9 Page 7 of 9 External & Internal angles of 2d regular shapes All of the external angles of regular 2d shapes add up to 360º We use this information to find the external (outside) angle of the shape. e.g. a triangle has 3 sides so each of the external angles are πππ π = πππ º 120º 120º 120º Following on from this, if you know that angles on a straight line equal 180º, then the Internal (inside) angles must be 180 β 120 = 60º A pentagon (5 sided) has external angles of πππ π = ππº The internal angles are therefore, 180 β 72 = 108º 108º 72º Exercise Complete the table (some may not be whole numbers. If not work to 1 d.p.) Sides 3 4 5 6 7 8 9 10 11 12 Name Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Unidecagon Dodecagon External Angle (º) 120 90 72 60 Internal Angle (º) 60 90 108 Page 8 of 9 Tessellation A shape is said to tessellate if a page can be covered with the shape WITH NO GAPS INBETWEEN THEM Initially these shapes look like they tessellate but you cannot add another row on without leaving gaps β so they DO NOT tessellate These shapes do tessellate as they leave no gaps in between them however many rows or columns you add Patterns can be made more interesting just by changing the colour of the shape but not the size or shape (congruency) Page 9 of 9