Table of Contents

## Triangle Inequality

Inequalities theorem Of Triangle: A triangle is a three-sided closed shape. The sum of the angles in a triangle is always 180 degrees. The side opposite the largest angle is called the hypotenuse. The other two sides are called the legs.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem is named after the Greek mathematician Pythagoras

## Triangle Inequality Definition

A triangle inequality is a statement that states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

## Inequalities theorem Of Triangle

The inequalities theorem of triangle states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. This theorem also known as the triangle inequality theorem.

The triangle inequality theorem is a simple yet important result in geometry. It used in many proofs, including the proof of the Pythagorean theorem. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. This theorem is also known as the triangle inequality theorem.

The triangle inequality theorem used in many proofs, including the proof of the Pythagorean theorem. The triangle inequality theorem also used in many other fields, such as physics and engineering.

## What is Triangle Inequality?

A triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

## Triangle Inequality Theorem

A triangle is a three-sided polygon. The three angles of a triangle always add up to 180 degrees. The three sides of a triangle are always in a straight line. The longest side of a triangle called the hypotenuse. The other two sides called the legs.

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

## Triangle Inequality Formula

The triangle inequality theorem states that the length of the hypotenuse of a right triangle is greater than the sum of the lengths of the other two sides. The theorem represented by the following equation:

$$ a + b > c $$

Where a, b, and c represent the lengths of the three sides of the triangle.

## Solved Examples

Question:

The average American family size is 2.54 people. Use the empirical rule to find the percentage of American families that have 2 or fewer people.

Solution:

The empirical rule states that 68% of all data points will fall within one standard deviation of the mean. This means that 68% of all American families have 2 or fewer people.