Test
The Pythagorean theorem
Dynamic tasks on legs, hypotenuse, rectangle diagonals, coordinate distance and practical applications.
Time left: 00:00:00
Sample questions
- The legs of a right triangle are ___ cm and ___ cm. Find the hypotenuse.
- A right triangle has hypotenuse ___ cm and one leg ___ cm. Find the other leg.
- Which set of three side lengths can form a right triangle?
- A rectangle has sides ___ cm and ___ cm. Find its diagonal.
- Find the distance between (___, ___) and (___, ___).
The Pythagorean theorem
In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: a² + b² = c². The hypotenuse lies opposite the right angle and is always the longest side. Find a missing leg by subtracting the known leg squared from c².
Applications
The theorem applies to rectangle diagonals, coordinate distances and practical length problems. Confirm that the triangle is right-angled, identify the hypotenuse and only then substitute values. The answer uses units of length, not square units.
Related mathematics tests
Quartiles and box plots
Dynamic tasks on medians, quartiles, interquartile range, outliers and reading box-and-whisker plots.
Systems of linear equations
Dynamic tasks on solving and checking systems, determining the number of solutions and modelling word problems.
Full Grade 8 test
Full Grade 8 mathematics test with mixed topics, dynamically selected questions and a choice of duration. Practise before an assessment or review the whole course at your own pace.
Pythagoras in solids
Dynamic tasks on space diagonals, cone slant height, pyramid apothem, sphere area and volume.
