What this quiz covers

Grade 8 Pythagoras Quiz 1 draws its questions at random from 21 questions across these topics:

• The Theorem — Naming Sides
• The Theorem — The Formula
• The Theorem — Areas of Squares
• Finding the Hypotenuse
• Finding a Shorter Side
• The Converse — Testing a Triangle
• Pythagorean Triples
• Pythagorean Triples — Multiples
• Word Problem — Ladder
• Word Problem — Rectangle Diagonal
• Word Problem — Distance
• Word Problem — TV Screen
• Word Problem — Flagpole Wire

Example questions

A sample of the questions you will practise in this quiz. Work them out yourself - the full solution appears after you answer each one.

1. Triangle PQR is right-angled at Q (see diagram). Which side is the hypotenuse?
2. In a right-angled triangle with legs \(a\) and \(b\) and hypotenuse \(c\), which statement is Pythagoras' Theorem?
3. Squares are drawn on all three sides of a right-angled triangle (see diagram). The squares on the two legs have areas 9 cm\(^2\) and 16 cm\(^2\). What is the area of the square on the hypotenuse?
4. A right-angled triangle has legs of 3 cm and 4 cm (see diagram). Find the length of the hypotenuse \(x\).
5. A right-angled triangle has legs of 5 cm and 12 cm (see diagram). Find the hypotenuse \(x\).