A triangle is a fundamental shape in geometry. It is a polygon that has exactly three sides, three vertices or corners, and three angles. Let me show you these basic components of a triangle.
The three vertices are the corner points where two sides meet. Here we can see vertices A, B, and C.
The three sides connect these vertices. Each side is a line segment between two vertices.
Finally, the three angles are formed where the sides meet at each vertex. These angles are the interior angles of the triangle.
Triangles can be classified in different ways. One common way is by the length of their sides. Let me show you the three main types.
An equilateral triangle has all three sides of equal length. This makes it perfectly symmetrical.
An isosceles triangle has exactly two sides of equal length. The two equal sides are called legs.
A scalene triangle has all three sides of different lengths. No two sides are equal in this type of triangle.
Triangles can also be classified by their angles. There are three types based on the size of their largest angle.
An acute triangle has all three angles less than 90 degrees. All angles are sharp and pointed.
A right triangle has exactly one angle that equals 90 degrees. This is called a right angle and is marked with a small square.
An obtuse triangle has one angle that is greater than 90 degrees. This large angle makes the triangle look wide and flat.
Triangles have several important mathematical properties that are always true, regardless of their size or shape.
The most fundamental property is that the sum of all three interior angles in any triangle always equals 180 degrees.
Let me demonstrate this with an equilateral triangle where each angle measures 60 degrees. When we add them up: 60 plus 60 plus 60 equals 180 degrees.
Another important property is the triangle inequality. This states that the sum of the lengths of any two sides must be greater than the length of the third side. This rule determines whether three given lengths can form a triangle.
To summarize what we have learned about triangles: A triangle is a fundamental geometric shape with three sides, three vertices, and three angles. We can classify triangles by their side lengths or by their angle measurements. Remember that the angles always sum to 180 degrees, and the triangle inequality helps us determine if three given lengths can actually form a triangle.