In this problem we will prove the Reverse Triangle Inequality Theorem, using what we have already proven In a previous problem- the Triangle Inequality. The Triangle Inequality theorem states that … [Read more...] about Reverse Triangle Inequality Theorem

# Triangle Inequalities

The triangle inequality theorem states that in any triangle, the sum of the lengths of any two sides is greater than the length of the thirds side.

So, for any triangle:

AB+BC>AC

AC+BC>AB

AC+AB>BC

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*Now that we've explained the basic concept of triangle inequalities in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## Hinge Theorem

What is the Hinge Theorem? Let's say you have a pair of triangles with two congruent sides but a different angle between those sides. Think of it as a hinge, with fixed sides, that can be opened to … [Read more...] about Hinge Theorem

## Converse of the Scalene Triangle Inequality

In today's lesson, we will prove the converse of the scalene triangle inequality. Using proof by contradiction, we will show that the side facing the larger angle is longer. Having proven the … [Read more...] about Converse of the Scalene Triangle Inequality

## The Scalene Inequality Theorem

A scalene triangle is a triangle in which all three sides have different lengths. The scalene inequality theorem states that in such a triangle, the angle facing the larger side has a measure larger … [Read more...] about The Scalene Inequality Theorem

## Triangle Inequality Theorem

We all know that "the shortest distance between two points is a straight line." That is the informal way of describing the Triangle Inequality Theorem. If we want to go from point A to point B, … [Read more...] about Triangle Inequality Theorem