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8 Constructions and Pythagoras’ theorem

Here are some reminders about the work you have already done on Key words
shapes and geometric reasoning.
Make sure you learn and
understand these key words:
To draw a regular polygon, you inscribed

Perpendicular lines meet at a need to know the lengths of the Pythagoras’ theorem
right angle (90°). You show that sides and the size of the internal
lines are perpendicular with a angles. internal angle
symbol that looks like the corner
of a square ( ).
Remember that in a regular
polygon all the sides are the
same length and all the internal
angles are the same size.

The perpendicular bisector of the The angle bisector of angle ABC
the line segment AB is the line is the line that cuts the angle
that passes through the exactly in half.
You can draw an angle bisector
midpoint of AB at right angles using only a straight edge and
to AB. perpendicular compasses. A angle bisector
bisector of AB these two angles
B B C are the same size
A

In this chapter you will learn about Pythagoras’ theorem.
Look at these diagrams.

Each diagram illustrates Pythagoras’ theorem. Look back at this page when you have !nished the

chapter and see if you can explain how they do that.
In this unit you will learn how to draw perpendicular lines from a point to a line and from a point on
a line. You will also learn how to draw shapes inside circles and use Pythagoras’ theorem to solve
two-dimensional problems.

8 Constructions and Pythagoras’ theorem 75