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Congruence and similarity are key concepts in Edexcel GCSE Mathematics. Two shapes are congruent if they are exactly the same shape and size. Two shapes are similar if they are the same shape but possibly different sizes — all corresponding angles are equal, and corresponding sides are in the same ratio. Higher tier students must also apply area and volume scale factors for similar shapes.
| Term | Meaning |
|---|---|
| Congruent | Identical in shape and size (one can be mapped to the other by reflection, rotation or translation) |
| Similar | Same shape, different size (one can be mapped to the other by an enlargement) |
| Scale factor | The multiplier that converts one length to the corresponding length in a similar shape |
| Corresponding | In matching positions in two shapes |
To prove two triangles are congruent, you must show one of these four conditions:
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