Triangle and Polygon
A polygon is indeed a 2-dimensional shape composed of straight sides, and by definition, it must have at least three sides. A triangle, being the simplest polygon, has exactly three sides and three angles. Therefore, it meets the criteria of being a polygon with the least number of sides, which is three.
A triangle is a polygon with three sides, three vertices, and three angles. It is one of the simplest shapes in geometry.
Type of triangle
We can group the types of triangles based on their side lengths and angle measures:
By Side Length:
Equilateral Triangle: All three sides are of equal length.
Isosceles Triangle: Two sides are of equal length.
Scalene Triangle: All three sides have different lengths.
By Angle Measure:
Acute Triangle: All angles are acute (less than 90 degrees).
Right Triangle: One angle is a right angle (measuring 90 degrees).
Obtuse Triangle: One angle is obtuse (greater than 90 degrees).
Properties of triangle
Triangles possess several properties, which are fundamental to their geometric nature and mathematical characteristics. Here are some key properties of triangles:
Three Sides: A triangle has exactly three sides.
Three Angles: A triangle has exactly three angles. The sum of the angles in any triangle is always 180 degrees.
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Angle Sum Property: The sum of the interior angles of a triangle is always 180 degrees.
Types by Angle Measure:
- Acute Triangle: All angles are less than 90 degrees.
- Right Triangle: One angle is exactly 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees.
Types by Side Length:
- Equilateral Triangle: All sides are equal.
- Isosceles Triangle: Two sides are equal.
- Scalene Triangle: All sides are different.
Height (Altitude): A perpendicular line segment drawn from one vertex to the opposite side (or its extension) is called the altitude of the triangle.
Median: A line segment connecting a vertex of the triangle to the midpoint of the opposite side is called a median. Each triangle has three medians, which intersect at the centroid of the triangle.
Perimeter: The perimeter of a triangle is the sum of the lengths of its three sides.
Area: The area of a triangle can be calculated using various formulas, such as
(1/2) × base × height, Heron's formula, or by trigonometric methods.