Class 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.In an isosceles triangle the two base angles are always...
- a) 60° each
- b) supplementary
- c) equal
- d) right angles
2.Two angles of a triangle are 50° and 60°. What is the third, in degrees?
3.Every angle of an equilateral triangle is the same size. How big is each one, in degrees?
4.Can a triangle have sides of 2 cm, 3 cm and 7 cm?
- a) Yes
- b) No — 2 and 3 together are shorter than 7
- c) Only if it is right-angled
- d) Only if it is isosceles
5.A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse, in centimetres?
6.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
- 3, 4, 5
- 2, 3, 4
- 5, 12, 13
- 9, 12, 15
- 4, 5, 6
- 8, 15, 17
7.An exterior angle of a triangle is 120°. One of the two opposite interior angles is 45°. What is the other, in degrees?
8.A right-angled triangle has an angle of 35° besides the right angle. What is the third angle, in degrees?

Answer key — Class 7 Maths — Properties of triangles

1. c) equal
2. 70
3. 60
4. b) No — 2 and 3 together are shorter than 7
5. 10
6. 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
7. 75
8. 55