Opposite angles are equal Alternate angles when a line is drawn to intersect parallel lines are equal. To recognise when this rule can be used look for ‘Z’ shapes. Supplementary or complementary angles when a line is drawn to intersect parallel lines add to 180 Degrees, soAgain look for ‘Z’ shapes. The supplementary angles are […]

## Bisecting a Line

To bisect a line AB, or cut it in half, we need to draw a line through the middle of the line AB, perpendicular to AB. We use a compass. Put the needle at A, open the compass to more that half the distance of the line AB and draw an arc through the line. […]

## The Distance Between Two Points

Suppose we want to find the length of the line between A and B in the diagram below. We draw a straight line between A and B, and make this rhe hypotenuse of a right angled triangle by drawing a horizontal line from A to a point directly below B and another line down from […]

## Scale Factors and Negative Enlargements

A ‘normal’ enlargement casts a ‘shadow’ of the shape, which may be larger or smaller than that shape to be enlarged. The scale factor k is positive, with the enlarged shape being k times as far from the centre of enlargement as the original shape. If the scale factor is more than one, the enlarged […]

## Trigonometry and Right Angled Triangles – Finding a Side

There are three basic formulae, involving the ratio of the lengths of the sides. Given a right angled triangle, we first label the sides for the angle we have: If we have the angle shown, we label the sides for this angle. Opposite =is the side opposite the angle x Hypotenuse =is the longest side, […]

## The Sine Rule

We can use the sine rule to 1.Find a side when it is opposite and a known angle and we also have another side opposite another angle, both of which we know: 2. Find an angle when it is opposite an known side and we also have another side opposite another angle, both of which […]