The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Pythagoras' theorem – worksheets to print
Work out the hypotenuse or a leg of a right-angled triangle, check whether a triangle is right-angled, and solve word problems: ladders, screens, space diagonals and the distance between two points.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Pythagoras' theorem: explained simply
In a right-angled triangle the three sides are linked: the squares on the two legs together are as big as the square on the hypotenuse. So you can work out the third side from the other two.
How to work it out
- The hypotenuse lies opposite the right angle and is the longest side. The other two sides are called legs.
- If the right angle is at C, then a² + b² = c². To find the hypotenuse: c = √(a² + b²). To find a leg: a = √(c² − b²).
- Converse: if the three sides of a triangle satisfy a² + b² = c², the triangle is right-angled.
An example, step by step
A right-angled triangle has legs a = 6 cm and b = 8 cm. How long is the hypotenuse c?
- Square the legs: 6² = 36 and 8² = 64.
- Add: c² = 36 + 64 = 100.
- Take the square root: c = √100 = 10 cm.
Understand other variations
Finding a leg
With c = 13 cm and a = 5 cm you subtract: b² = 13² − 5² = 169 − 25 = 144, so b = 12 cm.
Rounding
With a = 5 cm and b = 7 cm, c² = 25 + 49 = 74 and c = √74 ≈ 8.6 cm. Only round at the end.
Word problems
A 5 m ladder stands 1.4 m away from the wall: h² = 5² − 1.4² = 25 − 1.96 = 23.04, so it reaches h = 4.8 m high. Space diagonal of a cuboid: d² = a² + b² + c².
Distance between two points
P(1|2) and Q(7|10): the differences 6 and 8 are the legs, d² = 6² + 8² = 100, so d = 10.
Your turn
A screen is 40 cm wide and 30 cm high. How long is its diagonal?
Show the answer and method
d² = 40² + 30² = 1,600 + 900 = 2,500, so d = √2,500 = 50 cm.
Ready-made worksheets: Pythagoras' theorem
Click the picture to see the worksheet large and print it. “Use” opens it in the editor.