Page 95 - Mathematics Coursebook

8.4 Symmetry properties of triangles, special quadrilaterals and polygons

Worked example 8.4

a ‘I am a quadrilateral with one line of symmetry and rotational symmetry of order 1.
I have two pairs of sides of equal length, no parallel sides and one pair of equal angles.
What shape am I?’
b Describe the similarities and differences between a square and a rhombus.

a Kite One line of symmetry and rotational symmetry of order 1 could be a kite
or an isosceles trapezium. The other information tells you it could only
be a kite.
b All sides the same length Opposite angles in a square are equal, but they are all 90°.
This is not the case in the rhombus. They also have different symmetry
properties.

Similarities Differences
Opposite angles are equal All angles in a square are 90°.
This is not the case for a rhombus.
All sides the same length A square has four lines of symmetry.
A rhombus has no line symmetry.
Two pairs of parallel sides A square has order 4 rotational symmetry.
A rhombus has order 2 rotational symmetry.

) Exercise 8.4

1 Name the shapes that are being described.
a ‘I have three sides that are all the same length.
I have three equal angles.
I have three lines of symmetry and rotational symmetry of order 3.’
b ‘I have four sides.
I have one line of symmetry and rotational symmetry of order 1.
Two of my angles are equal.
I have two pairs of equal length sides.’
c ‘I have six sides.
All my sides are the same length.
I have six lines of symmetry and rotational symmetry of order 6.’

2 Describe the similarities between a rectangle and a parallelogram.
3 Describe the differences between an isosceles trapezium and a kite.

4 Match each description with the correct shape from the box. square isosceles triangle
a @) HAVE lVE LINES OF SYMMETRY AND ORDER ROTATIONAL SYMMETRY
b ‘I have no lines of symmetry and order 2 rotational symmetry.’ regular pentagon parallelogram
c ‘I have one line of symmetry and order 1 rotational symmetry.’ rectangle scalene triangle
d @) HAVE EIGHT LINES OF SYMMETRY AND ORDER ROTATIONAL SYMMETRY regular octagon
e ‘I have no lines of symmetry and order 1 rotational symmetry.’
f ‘I have four lines of symmetry and order 4 rotational symmetry.’
g ‘I have two lines of symmetry and order 2 rotational symmetry.’

94 8 Symmetry