Similarity & Congruence

Spec reference: Geometry and measures - Properties and constructions
Key idea: Identify congruent and similar shapes and use scale factors to find missing lengths, areas and volumes.

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Congruence

Two shapes are congruent if they are exactly the same shape and size (one could be flipped or rotated).

Conditions for congruent triangles

Condition	Meaning
SSS	Three sides equal
SAS	Two sides and included angle equal
ASA	Two angles and included side equal
RHS	Right angle, hypotenuse and one side equal

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Similarity

Two shapes are similar if they have the same shape but different sizes. Corresponding angles are equal and corresponding sides are in the same ratio.

Scale factors

If the linear scale factor is $k$:

$$\text{Area scale factor}=k^2$$$$\text{Volume scale factor}=k^3$$

Example

Two similar shapes have corresponding sides 4 cm and 10 cm. Find the ratio of their areas.

Linear scale factor $={\displaystyle \frac{10}{4}}=2.5$

Area scale factor $={2.5}^2=\boxed{{\displaystyle 6.25}}$

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Test Yourself

Question 1 of 5

Linear scale factor 3. Area scale factor?