All these rectangles are not similar to one another since Similar Figures shapes are similar only when Corresponding sides are in proportion AND Corresponding angles are equal All these rectangles are not similar to one another since only condition 2 is true

Similar Figures Scale Factor Corresponding sides are in proportion AND corresponding angles are equal Scale Factor Scale Factor is the number used as a multiplier in enlarging / reducing shapes To calculate the scale factor In similar shapes… …divide the length by length, and where possible breadth by breadth When Enlarging – Divide bigger length by smaller length When Reducing – Divide smaller length by bigger length

Similar Figures Enlargement Scale Factor = 16 ÷ 8 = 2 The rectangles below are similar: Find the scale factor of enlargement that maps A to B 8cm 16cm A B 5cm 10cm Enlargement Scale Factor = 16 ÷ 8 = 2

Similar Figures If we are told that two objects are similar, and we can calculate the scale factor, then we can calculate the value of an unknown side These 3 rectangles are similar. Find the unknown sides A B 8cm 24cm 3cm xcm Enlargement Scale Factor (A to B) = 24 ÷ 8 = 3 So x = 3 x E.S.F. = 3 x 3 = 9cm

Scale Factor applies to ANY SHAPES that are mathematically similar. Similar Figures Scale Factor applies to ANY SHAPES that are mathematically similar. 6 cm 1.4 cm 2cm y z 3 cm 12 cm 6 cm Given the shapes are similar, find the values y and z ? Enlargement Scale Factor = 12 ÷ 3 = 4 So Reduction Scale Factor must be ¼ Turn E.S.F upside down y = 2 x E.S.F = 2 x 4 = 8cm z = 6 x R.S.F = 6 x ¼ = 1.5cm

Scale factors Enlargement Scale factor? 8cm 8 12 12cm E.S.F = 12 ÷ 8 = 3 2 8cm 8 12 12cm Reduction Scale factor? 5cm R.S.F = 8 ÷ 12 = 2 3 7.5cm Can you see the relationship between the two scale factors?

By finding the Reduction Scale Factor find Scale factors Find a given Enlargement Scale Factor = 2 a = 9 x E.S.F = 9 x 2 = 18cm 9cm a b By finding the Reduction Scale Factor find the value of b. 15cm E.S.F turned upside down So b = 15 x ½ = 7.5cm R.S.F = ½

Scale factors Finding Unknown sides ccm bcm 20cm 6cm 12cm 18cm Since the Triangles have equal angles. The shapes are Mathematically Similar Enlargement Scale Factor = 18 ÷ 12 = 3 2 Therefore Reduction Scale Factor must be 2 3 b = 6 x E.S.F = 6 x 3 = 9cm c = 20 x R.S.F = 20 x 2 = 13.3cm 2 3

Ratio Simplifying a ratio ? Ratios can be used to compare different quantities Example : There are 2 triangles and 3 rectangles. The ratio of triangles to rectangles is said to be 2 : 3 Note: The ratio of rectangles to triangles is said to be 3 : 2

Simplifying a ratio is like simplifying fractions

Ratio Ratio Calculations Example : The ratio of boys to girls is 4:5. If there are 16 boys, how many girls are there. boys girls 4 5 x 4 x 4 16 20

Ratio Sharing Money Example : Bill and Ben share a raffle win of £400 in the ratio 3:5. How much does each get ? Step 1 : Since the ratio is 3:5, there are : 3+5 = 8 shares Step 2 : Each share is worth : Check ! 150 + 250 = 400 Step 3 : Bill gets 3 x 50 = £150 Ben gets 5 x 50 = £250