# Triangle and its properties

Contents

A triangle is a simple closed curve made of three line segments. It has three vertices, three sides and three angles.

5 exercises available

Let us recall here how we classify triangles into types based on the angles and the sides.

The sum of the three interior angles of a triangle is always 180 degrees. This property helps us solve a wide variety of problems based on Triangles.

Here we will learn two special types of triangles: Equilateral and Isosceles. A triangle in which all the three sides are of equal lengths and the measure of each angle is 60 degree is called an 'equilateral' triangle , whereas a triangle with two sides equal is called 'Isosceles'. Also, the angles opposite to equal sides of an isosceles triangle are equal and on the basis of this property, we are going to find missing angles of triangles. These also have the proofs for the properties of isosceles and equilateral triangles that use congruence of triangles. If you are yet to learn congruence, you can watch the proofs after you learn congruence of triangles.

The sum of the lengths of any two sides of a triangle is always greater than the third side. This is called Triangle Inequality Theorem.

A right-angled triangle is the one in which the measure of one of the angles is 90 degrees. In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. This is called Pythagorean Theorem. If the Pythagoras property holds, the triangle must be right-angled.

The Pythagorean theorem is one of the most famous ideas in all of mathematics. This tutorial proves it. Then proves it again... and again... and again. More than just satisfying any skepticism of whether the Pythagorean theorem is really true (only one proof would be sufficient for that), it will hopefully open your mind to new and beautiful ways to prove something very powerful.
Common Core Standard: 8.G.B.6