Pythagoras Theorem

With Pythagoras theorem we can find the lengths of a side in a right angled triangle given the other two sides. With the sides of the triangle as labelled above, we use the formula For example It is important to label the sides of the triangle a, b and c in the way shown above. […]

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The Cosine Rule

e can use the cosine rule to: 1.Find a side when it is opposite a known angle and that angle is between two known sides. 2. Find an angle when all three sides are known. 1. We start by labelling the sides a,b,c and the angles A,B,C with sides opposite their respective angles as shown. […]

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Circle Theorems – A Summary

The angle subtended at the centre of the circle is twice the angle subtended at the edge. The angle at the edge of a circle subtended by a diameter is a right angle. Opposite angles in a cyclic quadrilateral – where all the vertices are an the edge of the circle – add up to […]

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Quadrilaterals

A quadrilateral is a four sided shape. The internal angles for all quadrilaterals add up to 360 degrees. All shapes made up of four straight sides are quadrilaterals but some are special and are given special names. They are shown in the table below, along with their properties. Name Example Properties Square All the internal […]

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Working With Column Vectors

Writing vectors as column vectors is more informative than using vector notation since more information is included, and is preferable when working in the x – y plane. Suppose we have the triangle below. P splits AC in the ratio 1:2. The vector from A to B isand the vector from B to C is  […]

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