Geometry › Triangles

Triangles

Three sides, three angles, one rule that never breaks: those angles always add to 180°.

Triangle explorer

Drag any corner. The angles always add to 180°.

Isosceles, acute

Sum of angles

180°

always 180

∠A63°

∠B63°

∠C53°

By sides

Equilateral — all three sides equal. All angles 60°.
Isosceles — two sides equal, two angles equal.
Scalene — all sides different lengths.

By angles

Acute — all angles less than 90°.
Right — one angle exactly 90°.
Obtuse — one angle bigger than 90°.

Why 180°?

Cut the three corners off a paper triangle and place them next to each other along a straight line. They always fill exactly half a full turn. That's the whole proof, in scissors form.

Pythagoras' theorem

For a right triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two:

a² + b² = c²

So a triangle with legs of 3 and 4 has a hypotenuse of 5 (because 9 + 16 = 25).

Area

For any triangle: Area = ½ × base × height. Base and height must be perpendicular to each other.