What is an isosceles triangle?
An isosceles triangle has two sides the same length and two angles the same size.
The answer
An isosceles triangle has 3 sides, 3 vertices, no parallel sides and 1 line of symmetry. The angles inside an isosceles triangle add up to 180°.
Isosceles triangle diagram and properties
| Property | Count |
|---|---|
| Sides | 3 |
| Vertices (corners) | 3 |
| Angles add up to | 180° |
| Right anglesA right-angled isosceles triangle has 1. | 0 |
| Pairs of parallel sides | 0 |
| Lines of symmetry | 1 |
Key facts about the isosceles triangle
- The two equal angles are the ones at the bottom of the two equal sides.
- Its one line of symmetry runs from the top corner to the middle of the opposite side.
- Knowing one angle is only enough if you know where it is. 50° could be the top angle (giving 50°, 65° and 65°) or a base angle (giving 50°, 50° and 80°). An angle of 90° or more must be the top angle, because two of them would already make 180° or more.
Where you see it
The gable end of a house roof, a slice of pizza and a coat hanger are all close to isosceles triangles.
The common mistake
Putting the equal angles in the wrong place. They sit where each equal side meets the third side, not at the corner where the two equal sides meet.
An 11+ style question
An isosceles triangle has one angle of 50°. What could its other two angles be?
Answer: 65° and 65°, or 50° and 80°
- If 50° is the top angle, between the two equal sides, the other two share 180 − 50 = 130°, so each is 130 ÷ 2 = 65°.
- If 50° is a base angle, the other base angle is also 50°, and the top angle is 180 − 50 − 50 = 80°.
- Both triangles are possible, so a question must say or show which angle it means. Check which one before you calculate.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does an isosceles triangle have?
An isosceles triangle has 3 straight sides and 3 vertices (corners). Its angles add up to 180°.
How many lines of symmetry does an isosceles triangle have?
An isosceles triangle has 1 line of symmetry.
Can an isosceles triangle have a right angle?
Yes. A right-angled isosceles triangle has angles of 90°, 45° and 45°. Cutting a square in half along a diagonal makes two of them.
How do you say isosceles?
Eye-SOSS-uh-leez. It comes from Greek words meaning "equal legs".
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.