Grade 8 Math — 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.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
- 4, 5, 6
- 9, 12, 15
- 8, 15, 17
- 5, 12, 13
- 2, 3, 4
- 3, 4, 5
2.Every angle of an equilateral triangle is the same size. How big is each one, in degrees?
3.A right-angled triangle has a hypotenuse of 13 inches and one shorter side of 5 inches. How long is the other short side, in inches?
4.A right-angled triangle has shorter sides of 6 inches and 8 inches. How long is the hypotenuse, in inches?
5.In an isosceles triangle the two base angles are always...
- a) right angles
- b) 60° each
- c) supplementary
- d) equal
6.An isosceles triangle has an apex angle of 40°. How big is each base angle, in degrees?
7.Can a triangle have sides of 2 inches, 3 inches and 7 inches?
- a) Only if it is isosceles
- b) Only if it is right-angled
- c) Yes
- d) No — 2 and 3 together are shorter than 7
8.An exterior angle of a triangle is 120°. One of the two opposite interior angles is 45°. What is the other, in degrees?
Answer key — Grade 8 Math — Properties of triangles
- 1. 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
- 2. 60
- 3. 12
- 4. 10
- 5. d) equal
- 6. 70
- 7. d) No — 2 and 3 together are shorter than 7
- 8. 75