© boardworks ltd 2004 1 of 57 s2 2-d shapes ks3 mathematics
TRANSCRIPT
© Boardworks Ltd 2004 1 of 57
S2 2-D shapes
KS3 Mathematics
© Boardworks Ltd 2004 2 of 57
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Contents
S2 2-D shapes
S2.1 Triangles and quadrilaterals
S2.2 Polygons
S2.5 Circles
S2.3 Congruence
S2.4 Tessellations
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Labelling lines and angles in a triangle
When we label angles in a triangle we use capital letters to label the vertices, going round in order, clockwise or anticlockwise.
A
BC
a
b c
This triangle can be described as ABC.
The side opposite A is called side a.
The side opposite B is called side b.
The side opposite C is called side c.
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Labelling lines and angles in a triangle
How can we complete the labeling of this triangle?
?
? ?
r
This triangle is called PQR
P
q
Q
R p
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Right-angled triangle
Triangles are named according to their properties.
A right-angled triangle contains a right angle.
The longest side opposite the right angle is called the hypotenuse.
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Isosceles triangle
Triangles are named according to their properties.
An isosceles triangle has two equal sides.
Lines of symmetry are indicated with dotted lines.
The two base angles are also equal.
An isosceles triangle has one line of symmetry.
The equal sides are indicated by these lines.
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Equilateral triangle
Triangles are named according to their properties.
An equilateral triangle has three equal sides
An equilateral triangle has three lines of symmetryand has rotational symmetry of order 3.
and three equal angles.
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Scalene triangle
Triangles are named according to their properties.
A scalene triangle has no equal sides and no equal angles.
A scalene triangle does not have any lines of symmetry.
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What type of triangle is this?
This is a right-angled isosceles triangle.
It has one line of symmetry and no rotational symmetry.
Naming triangles
What symmetry properties does it have?
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Triangles on a 3 by 3 pegboard
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Quadrilaterals
Quadrilaterals are also named according to their properties.
A shape can be classified according to whether it has:
equal angles
right angles
diagonals that are at right angles
diagonals that bisect each other
equal and/or parallel sides
rotational symmetry.
line symmetry
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Parallelogram
In a parallelogram opposite sides are equal and parallel.
The diagonals of a parallelogram bisect each other.
A parallelogram has rotational symmetry of order 2.
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Rhombus
A rhombus is a parallelogram with four equal sides.
The diagonals of a rhombus bisect each other at right angles.
A rhombus has two lines of symmetry and it has rotational symmetry of order 2.
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Rectangle
A rectangle has opposite sides of equal length
A rectangle has two lines of symmetry.
and four right angles.
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Square
A square has four equal sides and four right angles.
It has four lines of symmetry and rotational symmetry of order 4.
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Trapezium
A trapezium has one pair of opposite sides that are parallel.
Can a trapezium have any lines of symmetry?
Can a trapezium have rotational symmetry?
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Isosceles trapezium
In an isosceles trapezium the two opposite non-parallel sides are the same length.
The diagonals of an isosceles trapezium are the same length.
It has one line of symmetry.
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Kite
A kite has two pairs of adjacent sides of equal length.
The diagonals of a kite cross at right angles.
A kite has one line of symmetry.
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Arrowhead
An arrowhead or delta has two pairs of adjacent sides of equal length and one interior angle that is more than 180°.
Its diagonals cross at right angles outside the shape.
An arrowhead has one line of symmetry.
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Quadrilateral family tree
This family tree shows how the quadrilaterals are related.
QUADRILATERAL
KITE PARALLELOGRAM TRAPEZIUM
RECTANGLE RHOMBUS
SQUARE
DELTA
ISOSCELES
TRAPEZIUM
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True or false
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?
Guess the shape
The shape is a kite.
Can you identify this shape from its properties?
Its diagonals cross at right angles.
It has one vertical line of symmetry.
None of its interior angles are more than 180°.
It has two pairs of adjacent sides of equal length.
It is a quadrilateral.
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?
Guess the shape
The shape is an isosceles trapezium.
Can you identify this shape from its properties?
Its diagonals are of equal length.
It has one vertical line of symmetry.
One pair of opposite, non-parallel sides are the same length.
It has one pair of parallel sides.
It is a quadrilateral.
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Quadrilaterals on a 3 by 3 pegboard