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Similarity and congruence
Similar shapes have the same shape but different sizes. Congruent shapes are identical.
Congruent triangles
Triangles are congruent if they match by one of these conditions:
SSS (three sides), SAS (two sides and the included angle), ASA (two angles and a side), RHS (right angle, hypotenuse, side).
SSS (three sides), SAS (two sides and the included angle), ASA (two angles and a side), RHS (right angle, hypotenuse, side).
Similar shapes
Corresponding angles are equal and lengths are in the same ratio.
Scale factor = new length ÷ old length
Use it to find missing sides.
Scale factor = new length ÷ old length
Use it to find missing sides.
Area and volume (Higher)
If the length scale factor is k:
area scale factor = k2
volume scale factor = k3
Lengths doubled → area × 4, volume × 8.
area scale factor = k2
volume scale factor = k3
Lengths doubled → area × 4, volume × 8.
Two similar triangles have corresponding sides 4 cm and 10 cm. Another side on the small triangle is 6 cm. Find the matching side on the large one.
- Scale factor = 10 ÷ 4 = 2.5
- 6 × 2.5 = 15
Answer: 15 cm
Congruent: SSS, SAS, ASA, RHS. Similar: same angles, lengths in proportion. Length factor k gives area factor k2 and volume factor k3.
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