Year 7 Maths — Properties of triangles

Use the angle sum, the exterior angle rule and Pythagoras' theorem in a triangle.

Name: ________________________

Before you start

A right-angled triangle, with the corner that makes it one marked. Find out what each of its three sides is called.

1. A short side
2. The other short side
3. Hypotenuse — the longest
4. The right angle

Square the two short sides, add them, and you land on the square of the hypotenuse — 60² + 80² = 100². Swapping which short side you call which changes nothing, because addition does not care about order.

1.Can a triangle have sides of 2 cm, 3 cm and 7 cm?
- a) Yes
- b) Only if it is isosceles
- c) No — 2 and 3 together are shorter than 7
- d) Only if it is right-angled
2.A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse, in centimetres?
3.Every angle of an equilateral triangle is the same size. How big is each one, in degrees?
4.Each row gives the three side lengths of a triangle. Sort them by whether the triangle is right-angled.
Groups: Right-angled · Not right-angled
- 8, 15, 17
- 2, 3, 4
- 5, 12, 13
- 9, 12, 15
- 3, 4, 5
- 4, 5, 6
5.A right-angled triangle has an angle of 35° besides the right angle. What is the third angle, in degrees?
6.A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. How long is the other short side, in centimetres?
7.In an isosceles triangle the two base angles are always...
- a) supplementary
- b) right angles
- c) equal
- d) 60° each
8.Two angles of a triangle are 50° and 60°. What is the third, in degrees?

Answer key — Year 7 Maths — Properties of triangles

1. c) No — 2 and 3 together are shorter than 7
2. 10
3. 60
4. 3, 4, 5 → Right-angled; 5, 12, 13 → Right-angled; 9, 12, 15 → Right-angled; 8, 15, 17 → Right-angled; 2, 3, 4 → Not right-angled; 4, 5, 6 → Not right-angled
5. 55
6. 12
7. c) equal
8. 70