Properties of Triangles
A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry. The sum of the interior angles of any triangle is always 180°.
Types of Triangles by Side Length
Equilateral Triangle
All three sides are equal, and all angles are 60°.
Isosceles Triangle
Two sides are equal, and the angles opposite those sides are equal.
Scalene Triangle
All sides and all angles are different.
Types of Triangles by Angle
Acute Triangle
All angles are less than 90°.
Right Triangle
One angle is exactly 90°.
Obtuse Triangle
One angle is more than 90°.
Basic Properties
- The sum of the interior angles is 180°.
- The length of one side is always less than the sum of the other two (Triangle Inequality Theorem).
- Every triangle has a perimeter (sum of all sides) and an area.
Examples
Example 1:
A triangle has angles 50°, 60°, and one unknown angle. What is the missing angle?
Solution:
Sum = 180° → 180 - (50 + 60) = 70°
Example 2:
Can a triangle have sides 5 cm, 7 cm, and 13 cm?
Solution:
Check the triangle inequality:
5 + 7 = 12, which is less than 13 ⇒ No, such a triangle is not possible.
Example 3:
Find the area of a triangle with base 8 cm and height 5 cm.
Solution:
Area = (1/2) × base × height = (1/2) × 8 × 5 = 20 cm²