A triangle is a polygon with three sides and three angles. Triangles are one of the most fundamental shapes in geometry and appear in many mathematical problems and real-life structures.
Triangles can be classified in two main ways:
- by their angles
- by their side lengths
Understanding these classifications helps us identify different triangles and study their properties.
Types of Triangles by Angles
An acute triangle has all three angles less than \(90^\circ\).
Right triangle
A right triangle has one angle equal to \(90^\circ\).
Obtuse triangle
An obtuse triangle has one angle greater than \(90^\circ\).
Types of Triangles by Sides
Triangles can also be classified according to their side lengths.
Scalene triangle
A scalene triangle has three sides of different lengths.
Isosceles triangle
An isosceles triangle has two equal sides. The angles opposite those sides are also equal.
Equilateral triangle
An equilateral triangle has three equal sides. Each angle is \(60^\circ\).
Triangle Inequality Rule
The Triangle Inequality Rule tells us whether three side lengths can form a triangle.
The sum of the lengths of any two sides must be greater than the third side.
Example:
Check if the side lengths \(3, 4,\) and \(5\) can form a triangle.
\(3 + 4 > 5\)
\(3 + 5 > 4\)
\(4 + 5 > 3\)
All conditions are satisfied, so these sides can form a triangle.
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