Grade 8 maths: Pythagoras, similarity and systems of equations

Geometry dominates Grade 8: right-angled triangles, similarity and the intercept theorem. At the same time the algebra becomes more demanding, because fractions and two unknowns appear.

Reference: existing NRW curriculum mapping in Germany. Topics and sequence may vary by federal state, school type and classroom. This selection is not a complete curriculum.

Before calculating, check whether a right angle is really given. For systems, substitution or elimination both work; write the result as a pair of values. Fractional equations always need a defined set of allowed values.

1. Calculate in right-angled triangles

Pythagoras’ theorem only holds in right-angled triangles: the squares on the two legs add up to the square on the hypotenuse. Always look for the hypotenuse opposite the right angle. The leg and altitude theorems split the same triangle into further relationships.

2. Similarity and the intercept theorem

Similar figures have equal angles and proportional sides. The intercept theorem compares segments on two rays cut by parallel lines. Check carefully which segments correspond to each other.

3. Rearranging terms and equations

Binomial formulas are used in reverse when factorising. Solve fractional equations by multiplying both sides by the common denominator, and exclude values that make a denominator zero. Two unknowns need two equations.