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© Boardworks Ltd 2004 1 of 57 S2 2-D shapes KS3 Mathematics

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© Boardworks Ltd 2004 2 of 57 A A A A A 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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© Boardworks Ltd 2004 3 of 57 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 B C a bc 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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© Boardworks Ltd 2004 4 of 57 Labelling lines and angles in a triangle How can we complete the labeling of this triangle? ? ? ? r This triangle is calledPQR P q Q R p

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© Boardworks Ltd 2004 5 of 57 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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© Boardworks Ltd 2004 6 of 57 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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© Boardworks Ltd 2004 7 of 57 Equilateral triangle Triangles are named according to their properties. An equilateral triangle has three equal sides An equilateral triangle has three lines of symmetry and has rotational symmetry of order 3. and three equal angles.

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© Boardworks Ltd 2004 8 of 57 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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© Boardworks Ltd 2004 9 of 57 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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© Boardworks Ltd 2004 10 of 57 Triangles on a 3 by 3 pegboard

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© Boardworks Ltd 2004 11 of 57 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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© Boardworks Ltd 2004 12 of 57 Parallelogram In a parallelogram opposite sides are equaland parallel. The diagonals of a parallelogram bisect each other. A parallelogram has rotational symmetry of order 2.

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© Boardworks Ltd 2004 13 of 57 Rhombus A rhombus is a parallelogramwith 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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© Boardworks Ltd 2004 14 of 57 Rectangle A rectangle has opposite sides of equal length A rectangle has two lines of symmetry. and four right angles.

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© Boardworks Ltd 2004 15 of 57 Square A square has four equal sidesand four right angles. It has four lines of symmetry and rotational symmetry of order 4.

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© Boardworks Ltd 2004 16 of 57 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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© Boardworks Ltd 2004 17 of 57 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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© Boardworks Ltd 2004 18 of 57 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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© Boardworks Ltd 2004 19 of 57 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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© Boardworks Ltd 2004 20 of 57 Quadrilateral family tree This family tree shows how the quadrilaterals are related. Q UADRILATERAL K ITE P ARALLELOGRAM T RAPEZIUM R ECTANGLE R HOMBUS S QUARE D ELTA I SOSCELES T RAPEZIUM

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© Boardworks Ltd 2004 21 of 57 True or false

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© Boardworks Ltd 2004 22 of 57 ? 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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© Boardworks Ltd 2004 23 of 57 ? 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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© Boardworks Ltd 2004 24 of 57 Quadrilaterals on a 3 by 3 pegboard

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