Download Triangles

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
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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
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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
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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 “pushed over” is called a Parallelogram
It has opposite sides and opposite angles the same size
A square that looks like it has been “pushed over” 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
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Exercise
Name the Quadrilaterals from the word list
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Congruency & Similarity
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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
𝟑𝟔𝟎
𝟑
= 𝟏𝟐𝟎 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 – 120 = 60º
A pentagon (5 sided) has external angles of
𝟑𝟔𝟎
𝟓
= 𝟕𝟐º
The internal angles are therefore, 180 – 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
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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 – 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)
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