BitWithBite
Geometry · Quick Reference
Triangles Cheat Sheet
In one line: a triangle is the simplest possible polygon, with just three sides and three angles — yet it's central to almost every area of geometry and trigonometry.
Key Ideas
1Triangle Angle Sum. The three interior angles of any triangle always add up to exactly 180°.
2Classifying by Sides. Equilateral (all 3 sides equal), isosceles (exactly 2 sides equal), scalene (no sides equal).
3Classifying by Angles. Acute triangle (all angles < 90°), right triangle (one angle = 90°), obtuse triangle (one angle > 90°).
4The Triangle Inequality. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, or the triangle can't exist.
5The Pythagorean Theorem. For a right triangle with legs a and b and hypotenuse c: a^2 + b^2 = c^2.
Worked Examples
A triangle has angles 50° and 70°. Find the third angle.
60°
A right triangle has legs 3 and 4. Find the hypotenuse.
c = 5
Can a triangle have sides 2, 3, and 10?
No, this triangle cannot exist
Formulas
Angle sum: A + B + C = 180°
Pythagorean theorem: a^2 + b^2 = c^2
Practice Yourself
A triangle has angles 60° and 60°. Find the third angle.
60°
A right triangle has legs 6 and 8. Find the hypotenuse.
10
Classify a triangle with sides 5, 5, 5.
Equilateral