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Trigonometry Introduction Aims: To understand the effects of enlargements on shapes and the properties of similar shapes. To be able to understand that the angles are conserved in similar shapes and that the ratio of the side lengths is fixed for each angle To be aware of the links between the ratio of side lengths and the angles in a right angled triangle and the trigonometric rules. Starter Which are congruent and similar shapes? What makes the shapes congruent and similar? What is the same and what is different between similar shapes? Activity 1 Look at similar triangles by cutting A4, A5, A6, A7 paper diagonally, they will produce triangles with the same angle. Discuss what will happen if we double the sides etc. What is the relationship between the sides, ratios, decimals? Is this the same for all of these triangles? Activity 2 Try a different set of triangle with the vertical and horizontal sides in a ratio of 2:1 or 3:2 etc. Will you always get the same angles? Is the ratio or decimal the same? How does the decimal change? Discover that each angle has its own ratio. Extension: does this ratio work for other pairs of sides? Hypotenuse and adjacent, hypotenuse and opposite? Plenary Discuss the group’s findings and the connections between the different triangles, sides, angles and ratios. Introduce the concepts of different names for these ratios and the words Sine, Cosine and Tangent. To be explored next lesson. Helen Statton 1 565342280