What is a right-angled triangle?
A right-angled triangle is a triangle with one angle of exactly 90°, a right angle.
The answer
A right-angled triangle has 3 sides, 3 vertices and no parallel sides. The one drawn here has 0 lines of symmetry. A right-angled isosceles triangle has 1. The angles inside a right-angled triangle add up to 180°.
Right-angled triangle diagram and properties
| Property | Count |
|---|---|
| Sides | 3 |
| Vertices (corners) | 3 |
| Angles add up to | 180° |
| Right angles | 1 |
| Pairs of parallel sides | 0 |
| Lines of symmetryA right-angled isosceles triangle has 1. | 0 |
Key facts about the right-angled triangle
- The other two angles always add up to 90°, because 180 − 90 = 90.
- A triangle can never have two right angles: the two would already make 180°.
- The right angle is shown with a small square in the corner.
- Its area is half of the rectangle it fits in: ½ × base × height.
Where you see it
A set square, a slice of toast cut corner to corner and the side of a ramp against a wall.
The common mistake
Calling the longest side the height. The height is one of the two sides that meet at the right angle, not the sloping side.
An 11+ style question
One angle of a right-angled triangle is 38°. What is the third angle?
Answer: 52°
- One angle is 90°, so the other two add up to 180 − 90 = 90°.
- 90 − 38 = 52, so the third angle is 52°.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does a right-angled triangle have?
A right-angled triangle has 3 straight sides and 3 vertices (corners). Its angles add up to 180°.
How many lines of symmetry does a right-angled triangle have?
A right-angled triangle like the one drawn here has 0 lines of symmetry. A right-angled isosceles triangle has 1.
How do you find the area of a right-angled triangle?
Multiply the two sides that meet at the right angle and halve the answer. A right-angled triangle with sides of 6 cm and 4 cm around the right angle has an area of 6 × 4 ÷ 2 = 12 cm².
Shape questions are quick marks in the 11+
Angles, symmetry, nets and 3D shapes come up in 11+ maths and non-verbal reasoning. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.