① Scale factorsNo calculator
Two shapes are similar if one is an enlargement (or a reduction) of the other. Pick a pair of matching sides, then divide the length on the new shape by the length on the original shape. For a reduction the scale factor is a fraction.
② Finding missing lengthsNo calculator
Find a pair of matching sides where both lengths are known and work out the scale factor. Then multiply to go to the larger shape, or divide to go back to the smaller shape. Some shapes are turned round, so check which sides match.
③ Similar trianglesNo calculator
Parallel lines make equal angles, so the two triangles are similar. Match up the sides, find the scale factor, then use it. Sometimes you need to add two lengths together, or take one away, to get the side you need.
④ Using similar shapes to solve problemsNo calculator
The picture only sets the scene. Sketch the two similar shapes, label the lengths you know, find the scale factor, then use it to find the length you want.
⑤ Area and volume scale factorsNo calculatorExtension
If every length is multiplied by a scale factor k, then every area is multiplied by k² and every volume is multiplied by k³. Work out the length scale factor first.
Key steps
Scale factor: divide a length on the new shape by the matching length on the original shape.
Matching sides: sides in the same position on the two shapes. They are opposite equal angles. Turn or sketch the shapes if you are unsure.
Using it: to find a length on the larger shape, multiply by the scale factor. To find a length on the smaller shape, divide.
Parallel lines make equal angles, so a triangle cut by a line parallel to one side gives two similar triangles.
Areas and volumes: if the lengths are multiplied by k, areas are multiplied by k² and volumes by k³.