Unit 9 Section 1 : 2-D Shapes

The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes.

Rectangle All angles are right angles (90°) Opposite sides have the same length
Square the same length All angles are right angles (90°)
Parallelogram Opposite sides have the same length
Rhombus All the sides have the same length Diagonals bisect at right angles
Trapezium
Kite Diagonals intersect at right angles
Isosceles Triangle Two sides have the same length and the angles opposite these two sides are equal
Equilateral Triangle All angles are 60°

Example 1

Draw the lines of symmetry of an equilateral triangle.

There are 3 lines of symmetry, as shown in the diagram. They join each vertex (corner) to the midpoint of the opposite side.

Example 2

Name each of the following shapes:

(a)

This is a rhombus because all the sides have the same lengths.

(b)

This is an isosceles triangle because two of the angles are the same size.

Example 3

State the order of rotational symmetry of:

(a)a trapezium,
1
(b)a parallelogram.
2 (unless the parallelogram happens to be a square, in which case the order of rotational symmetry would be 4).

Exercises

Question 1

Name each of the following shapes:

(a)
(b)
(c)
(d)
(e)
(f)
Question 2

Show the lines of symmetry of:

(a)
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(b)
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(c)
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(d)
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Question 3

How many lines of symmetry are there for:

(a)
a parallelogram,
(b)
a rhombus ?
Question 4

State whether each of the following statements is true or false.

(a)A square is also a rhombus.
(b)A square is also a kite.
(c)A rectangle is also a kite.
(d)A parallelogram is also a kite.
(e)A rectangle is also a parallelogram.
Question 5

Write down the order of rotational symmetry of:

(a)a rhombus
(b)a square,
(c)an isosceles triangle,
(d)an equilateral triangle,
(e)a kite.
Question 6

A triangle has one line of symmetry. What type of triangle is it?

Question 7

How many symmetry lines have the following trapeziums?

Question 8

A right-angled triangle is also an isosceles triangle. What sizes are the other angles in this triangle?

°
Question 9

For a semicircle:

(a)

show its lines of symmetry,

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(b)

state its order of rotational symmetry.

Question 10

(a)

Show the lines of symmetry of a regular pentagon.

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(b)

State the order of rotational symmetry of a regular octagon.

Question 11

Rosemary drew these rectangles using a computer:

Rectangle A has width 3 and length 5:

The computer repeated these instructions to draw the other rectangles:

new width = previous width × 2

new length = previous length + previous width

Complete this table.

widthlength
rectangle A35
rectangle B
rectangle C
rectangle D