Foundation and Higher · similar shapes

Similar shapes:
one number unlocks every missing side.

find the
scale factor

first, the word itself —

Similar

same shape, different size

every length × the same number

step 1 of 2

Find the scale factor

1. Match a pair of sides you know: 6 and 9.

2. Big ÷ small: 9 ÷ 6 = 1.5.

✓ Scale factor = 1.5

step 2 of 2

Use it both ways

1. Small to big, multiply: x = 4 × 1.5 = 6 cm.

2. Big to small, divide: y = 7.5 ÷ 1.5 = 5 cm.

✓ Every length uses the same
scale factor

one number does it all —

Scale factor

big ÷ small, matching sides

Small to big

multiply

Big to small

divide

The angles never change —
only the lengths are scaled.

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