2D shape and pattern
Types of triangles
Triangles are the strongest shape in building — and every polygon can be broken into them. Their names come from their sides.
Naming triangles by their sides
EQUILATERAL — all three sides equal, and all three angles equal too. ISOSCELES — two sides equal, and the two angles opposite them equal. SCALENE — all three sides different, and all three angles different. Count the equal sides and the name follows.
Naming triangles by their angles
RIGHT-ANGLED — has one angle of exactly 90°. ACUTE — all three angles are less than 90°. OBTUSE — has one angle greater than 90°. A triangle can have both kinds of name at once: a triangle can be right-angled AND isosceles.
What is impossible
The three angles of a triangle always add to 180°. That rules some things out straight away. Can a triangle have TWO right angles? No — 90 + 90 = 180 already, leaving nothing for the third angle. Can it have THREE right angles? Definitely not. Can it have two obtuse angles? No — two angles over 90° would already pass 180°. So a triangle can have at most ONE right angle and at most ONE obtuse angle.
Sketching them
Use a pencil and ruler, and check with your partner by tracing and comparing the angles. Most people find the EQUILATERAL triangle hardest to draw. That is because all three sides must be exactly equal — get one slightly wrong and it becomes isosceles instead. Scalene is easiest: nothing has to match.
Worked examples
Naming a triangle with two equal sides
- Count the sides that are equal in length.
- Two of them match.
- Two equal sides means isosceles.
Answer: It is an isosceles triangle
Naming a triangle with no equal sides
- Check each side against the others.
- All three are different lengths.
Answer: It is a scalene triangle
Can a triangle have two right angles?
- Two right angles would be 90° + 90° = 180°.
- But all three angles must total 180°.
- That leaves 0° for the third angle, which is impossible.
Answer: No — a triangle can have at most one right angle
How many acute angles must every triangle have?
- Suppose a triangle has an obtuse angle, say 100°.
- The other two must share 80° between them.
- So both must be acute.
Answer: Every triangle has at least two acute angles
Where you see this in real life
- Bridges and roof trusses are built from triangles because the shape cannot be pushed out of place.
- A ladder leaning on a wall makes a right-angled triangle with the wall and the ground.
- Road signs warning of a hazard are equilateral triangles — all three sides the same.
Key words
- Equilateral triangle
- A triangle with all three sides equal.
- Isosceles triangle
- A triangle with two sides equal.
- Scalene triangle
- A triangle with all three sides different.
- Right angle
- An angle of exactly 90°.
- Acute angle
- An angle smaller than 90°.
- Obtuse angle
- An angle bigger than 90° but smaller than 180°.