01 Key Concepts
Triangle Angle Sum
The three interior angles of any triangle always add up to exactly 180°.
Classifying by Sides
Equilateral (all 3 sides equal), isosceles (exactly 2 sides equal), scalene (no sides equal).
Classifying by Angles
Acute triangle (all angles < 90°), right triangle (one angle = 90°), obtuse triangle (one angle > 90°).
The 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.
The Pythagorean Theorem
For a right triangle with legs a and b and hypotenuse c: a^2 + b^2 = c^2.
02 Key Formulas
- Angle sum: A + B + C = 180°
- Pythagorean theorem: a^2 + b^2 = c^2
03 Solved Examples
Example 1 A triangle has angles 50° and 70°. Find the third angle.
- All three angles sum to 180°.
- 180 - 50 - 70.
Answer: 60°
Example 2 A right triangle has legs 3 and 4. Find the hypotenuse.
- Apply the Pythagorean theorem: c^2 = a^2+b^2 = 3^2+4^2 = 9+16 = 25.
- c = sqrt(25).
Answer: c = 5
Example 3 Can a triangle have sides 2, 3, and 10?
- Check the triangle inequality: 2+3=5, which must be greater than the third side.
- 5 is not greater than 10.
Answer: No, this triangle cannot exist
04 Practice Questions
1A triangle has angles 60° and 60°. Find the third angle.
60°
2A right triangle has legs 6 and 8. Find the hypotenuse.
10
3Classify a triangle with sides 5, 5, 5.
Equilateral
4Classify a triangle with sides 4, 4, 7.
Isosceles
5Can a triangle have sides 1, 2, 3?
No, since 1+2=3 is not greater than 3
📄 Triangles — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.