Pie Charts: How to Draw, Calculate Angles + Examples
Math Education7 min read
Math Education
7 min read
Types of Triangle by Sides and Angles + Their Properties
Published: 12.08.2026·Updated: 12.08.2026
Dewi Lestari
Mathematics Specialist
A triangle is a plane shape bounded by three sides with three angles. Triangles are classified in two separate ways: by side length and by angle size. Every triangle therefore carries two names at once — and that is what confuses children most.
Classified by Sides
| Type | Feature | Properties |
|---|---|---|
| Equilateral | All three sides equal | All angles 60°, 3 lines of symmetry |
| Isosceles | Two sides equal | Two base angles equal, 1 line of symmetry |
| Scalene | All sides different | All angles different, no line of symmetry |
Classified by Angles
| Type | Feature |
|---|---|
| Acute | All three angles under 90° |
| Right-angled | One angle exactly 90° |
| Obtuse | One angle over 90° |
Note the word one: a triangle cannot have two right angles, because that already totals 180° and leaves nothing for the third.
One Triangle, Two Names
This is where most mistakes happen. Every triangle has a name from both categories:
- Sides 3, 4, 5 cm → scalene and right-angled
- Sides 5, 5, 8 cm → isosceles and obtuse
- Sides 6, 6, 6 cm → equilateral and acute
When a question asks "what kind of triangle is this?", the answer often needs both. See also types of angle.
The Angles Always Total 180 Degrees
The single rule used most often in questions:
Example: two angles of a triangle are 65° and 40°. What is the third?
180 − 65 − 40 = 75°
A way to prove it at home: cut a triangle from paper, tear off all three corners, and lay them side by side. They form a straight line, which is 180°. A child who has done this never doubts the rule again.
Can Any Three Lengths Form a Triangle?
Not always. The condition: the two shortest sides must add to more than the longest.
- 3, 4, 5 → 3 + 4 = 7 > 5 ✔ works
- 2, 3, 9 → 2 + 3 = 5 < 9 ✘ does not
It makes physical sense: if two short sticks joined together are still shorter than the third, their ends can never meet.
The Basic Formulas
- Perimeter = side a + side b + side c
- Area = ½ × base × height
More detail in how to find the area of a triangle. For right-angled triangles, the sides are governed by the Pythagorean theorem.
The Mistakes That Actually Cost Marks
1. Treating "isosceles" and "acute" as mutually exclusive. They belong to different categories, so one triangle can be both. This is the number one cause.
2. Using a slanted side as the height. The height must be perpendicular to the base. In an obtuse triangle it can even fall outside the shape.
3. Forgetting the half in the area formula. The answer comes out exactly double — an instantly recognisable pattern.
4. Assuming any three lengths make a triangle. A classic trap with numbers like 2, 3, 9.
5. Thinking an equilateral triangle has 90° angles. All three are 60°, since 180 divided by 3.
