Triangle Inequality Theorem
What is the Triangle Inequality Theorem?
Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Can an Equilateral Triangle Violate the Triangle Inequality Theorem?
No, equilatral triangle can’t voilate the Triangle Inequality Theorem. As all sides in Equilateral Triangle are equal and sum of any two sides is twice the third i.e., greater than the third side.
What is the Converse of the Triangle Inequality Theorem?
Converse of the Triangle Inequality Theorem states that if sum of the lengths of any two sides of a triangle is greater than the length of third side, then given three sides can form a triangle.
What is the Triangle Inequality for Angles?
The Triangle Inequality for Angles states that the sum of any two angles in a triangle must be greater than the measure of the third angle.
What is the Relationship between the Sides of a Right Triangle?
The relationship between the sides of a right-angle triangle is given by the Pythagoras Theorem. If the sides of right-angle triangle are a, b, and c (c is the greatest side) then by Pythagoras theorem:
a2 + b2 = c2
Triangle Inequality Theorem, Proof & Applications
Triangle Inequality Theorem is the relation between the sides and angles of triangles which helps us understand the properties and solutions related to triangles. Triangles are the most fundamental geometric shape as we can’t make any closed shape with two or one side. Triangles consist of three sides, three angles, and three vertices.
The construction possibility of a triangle based on its side is given by the theorem named “Triangle Inequality Theorem.” The Triangle Inequality Theorem states the inequality relation between the triangle’s three sides. In this article, we will explore the Triangle Inequality Theorem and some of its applications as well as the other various inequalities related to the sides and angles of triangles.
In this article, we’ll delve into the concept of triangle inequality, the triangle inequality theorem, its significance, and its practical applications.
Table of Content
- What is Triangle Inequality Theorem?
- Triangle Inequality Theorem Formula
- Triangle Inequality Theorem Proof
- Triangle Inequality Theorem – Applications & Uses
- How to Identify Triangles
- How to Find Range of Possible Values of Sides of Triangle
- Various Inequalities in Triangle
- Sample Problems on Triangle Inequality Theorem
- Practice Problem on Triangle Inequality Theorem