Explore and identify the characteristics of some quadrilaterals

MATHEMATICS

Grade 9

QUADRILATERALS, PERSPECTIVE DRAWING,TRANSFORMATIONS

Module 21

EXPLORE AND IDENTIFY THE CHARACTERISTICS OF SOME QUADRILATERALS

ACTIVITY 1

To explore and identify the characteristics of some quadrilaterals

[LO 3.4]

In this work, you will learn more about some very important quadrilaterals. We need to know their characteristics as they occur often in the natural world, but especially in the manmade environment.

You will have to measure the lengths of lines and the sizes of angles, so you will need to have your ruler and protractor ready. For cutting out quadrilaterals you will need a pair of scissors.

First we start with the word quadrilateral. A quadrilateral is a flat shape with four straight sides, and, therefore four corners. We will study the sides (often in opposite pairs), the internal angles (also sometimes in opposite pairs), the diagonal lines and the lines of symmetry.

Look out for new words, and make sure that you understand their exact meaning before you continue.

1. Lines of symmetry

You have already encountered the quadrilateral we call a square.

The square

From your sheet of shapes, cut out the quadrilateral labelled “SQUARE”. Fold it carefully so that you can determine whether it has any lines of symmetry.

Lines of symmetry are lines along which any shape can be folded so that the two parts fall exactly over each other.

Make sure that you have found all the different lines of symmetry. Then mark the lines of symmetry as dotted lines on the sketch of the square alongside, using a ruler. One of them has been done as an example.

The dotted line in the sketch is also a diagonal, as it runs from one vertex (corner) to the opposite vertex.

- Look around you in the room. Can you find a square shape quickly?

If we push the square sideways, without changing its size, it turns into a rhombus.

1.2 The rhombus

Identify the RHOMBUS from the sheet of shapes. It is clear that it looks just like a square that is leaning over. Cut it out so that you can fold it to find its lines of symmetry.

Again, draw dotted lines of symmetry on this diagram

- Is the dotted line in this sketch a line of symmetry?

If we take a rhombus and stretch it sideways, then a parallelogram is produced.

1.3 The parallelogram

Find the PARALLELOGRAM on the sheet of shapes.

Cut it out so that you can fold it to find any lines of symmetry; draw them as dotted lines.

- You might have to search a bit to find something in the shape of a parallelogram. Your homework is to see whether you can find one in 24 hours.

This parallelogram turns into a rectangle when we push it upright.

1.4 The rectangle

Cut out the RECTANGLE and find its lines of symmetry to fill in on the rectangle alongside.

- Write down the differences you see between the rectangle and the square.

Now take the two end sides of the rectangle and turn them out in different directions to form a trapezium.

1.5 The trapezium

There is more than one TRAPEZIUM on the shape sheet. This is another example of a trapezium. Again, cut them out and find lines of symmetry.