Pythagoras' Theorem

Mathematics · Geometry · ages 13-14

Name ______________________ Date ____________

A right-angled triangle has shorter sides of 6 m and 8 m. What is the hypotenuse?
- 10
- 14
- 48
- 7
A right-angled triangle has shorter sides of 3 cm and 4 cm. What is the length of the hypotenuse in cm?
Answer: ______________
In a right-angled triangle, which side is called the hypotenuse?
- The side opposite the right angle
- Either of the two shorter sides
- The side that looks the shortest
Pythagoras' Theorem works on every triangle, not just right-angled ones.
Circle one: True False
A right-angled triangle has a hypotenuse of 10 cm and one shorter side of 6 cm. What is the other shorter side?
- 8
- 4
- 16
- 12
Point A is at (0, 0) and point B is at (3, 4) on a grid. What is the distance from A to B?
- 5
- 7
- 12
A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. What is the other shorter side in cm?
Answer: ______________
What is the distance between the points (1, 1) and (4, 5)?
- 5
- 7
- 12
- 25
A 10 m ladder leans against a wall with its foot 6 m from the wall. How far up the wall does the ladder reach?
- 8 m
- 4 m
- 16 m
- 12 m
Maya has a right-angled triangle with hypotenuse 17 and one shorter side 8. She works out the other side as 17 - 8 = 9. What mistake did she make?
- She used the wrong hypotenuse value
- She made no mistake
- She subtracted the sides directly instead of using their squares

Answer key

For grown-ups. Fold this page away before handing over the rest.

10 · 6 squared + 8 squared = 36 + 64 = 100, and the square root of 100 is 10.
5 · With legs 3 and 4, c squared = 9 + 16 = 25, so the hypotenuse is 5.
The side opposite the right angle · The hypotenuse is the longest side. It sits opposite the right angle.
False · It only works when the triangle has a right angle. Without one, a² + b² does not equal c².
8 · 100 - 36 = 64, and the square root of 64 is 8.
5 · The gap is 3 across and 4 up, so the distance is the square root of 3² + 4², which is 5.
12 · 13 squared - 5 squared = 169 - 25 = 144, so the missing side is 12.
5 · Across: 4 - 1 = 3. Up: 5 - 1 = 4. Then 9 + 16 = 25, so the distance is 5.
8 m · 100 - 36 = 64, so the ladder reaches 8 m up the wall.
She subtracted the sides directly instead of using their squares · She should square first: 17² - 8² = 289 - 64 = 225, so the missing side is 15, not 9.