You've looked a lot at shapes in KS3 Maths. This particular quiz on shapes looks at the special number relationship linking the lengths of the sides of a right-angled triangle. This relationship is named after the ancient Greek mathematician, Pythagoras.

Pythagoras' Theorem says that, in right-angled triangles: 'The square on the hypotenuse (that's the longest side which will be opposite the right angle) is equal to the sum of the squares on the other two sides'. Because this rule is true for every right-angled triangle, you can use it to test whether a triangle whose angles you don't know (so long as you do know the lengths of the sides) has a right angle. That will come in handy in this quiz!

You may find it helpful to draw some diagrams while doing this quiz. So, get your pencil and paper out and see how well you can do. Take your time and read each question carefully before you choose your answers. Good luck!

1.

A right-angled isosceles triangle has hypotenuse of length 15 cm. What are the angles at either end of the hypotenuse?

15^{o} and 75^{o}

30^{o} and 60^{o}

45^{o} and 45^{o}

20^{o} and 70^{o}

2.

If the longest side of a right-angled triangle is c cm and the other sides are a cm and b cm, Pythagoras' Theorem states that .......

a^{2} x b^{2} = c^{2}

(a + b)^{2} = c^{2}

a^{2} + b^{2} = c^{2}

a^{2} - b^{2} = c^{2}

Remember, Pythagoras' Theorem only applies to right-angled triangles

3.

The hypotenuse of a right-angled triangle is 26 cm. One of the shorter sides is 10 cm. How long is the third side?

30 cm

24 cm

16 cm

8 cm

26^{2} - 10^{2} = 24^{2}

4.

The foot of a ladder of length 3.75 m is 1.4 m away from a vertical wall. How high up the wall will the ladder reach (to the nearest 1 cm)?

3.84 m

3.48 m

3.24 m

3.18 m

This assumes that the ground is perfectly level!

5.

In a triangle, base 25 cm and height 12 cm, the perpendicular from the base to the opposite vertex divides the base in the ratio 3:2. How long are the other two sides (to 1dp)?

15.6 cm and 19.2 cm

16.3 cm and 18.9 cm

15.6 cm and 16.3 cm

18.9 cm and 19.2 cm

Split the triangle into two right-angled triangles with bases 15 cm and 10 cm

6.

A rectangle has length 2.4 m and width 0.7 m. How long is its diagonal?

2.0 m

2.5 m

3.0 m

3.5 m

The diagonal is the hypotenuse of a right-angled triangle

7.

The cross-section of a porch roof is an isosceles triangle with height 0.8 m and base 3.0 m. How long is each sloping roof section?

3.1 m

2.3 m

1.9 m

1.7 m

I hope you remembered the rules for isosceles triangles

8.

A triangle has sides of length 4 cm, 5 cm and 6 cm. Which of these statements is not true?

The three angles add up to 180^{o}

All three angles are acute

The triangle is scalene

The largest angle is 90^{o}

(4 x 4) + (5 x 5) = 41 but 6 x 6 = 36 so the triangle cannot contain a right angle

9.

The following sets of numbers represent the lengths of the sides of a triangle. Which is not a right-angled triangle?

15, 20, 25

18, 24, 30

16, 30, 36

15, 36, 39

Trial and error is a very useful tool in maths

10.

In a right-angled triangle the sides forming the 90^{o} angle are 6 cm and 8 cm. What is the length of the third side?

10 cm

12 cm

14 cm

16 cm

36 + 64 = 100; √100 = 10. The longest side in a right-angled triangle is called the hypotenuse

^{o}