"Equidistant" means the same distance (from the prefix "equi-", which means equal, and "distance"). Parallel lines are equidistant from each other. This means that every point on one line is always … [Read more...] about Parallel Lines are Equidistant

## Reverse Triangle Inequality Theorem

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

## Find the area of a parallelogram using diagonals

In another problem, we found the area of a parallelogram whose diagonals were perpendicular using the lengths of those diagonals and the lengths of one of its sides. We actually only needed the … [Read more...] about Find the area of a parallelogram using diagonals

## Area of a Right Triangle

This post will be a short and simple but very useful application of the general formula for finding the area of a triangle, to the specific case of a right triangle. Problem ΔABC is a right … [Read more...] about Area of a Right Triangle

## A Parallelogram with Perpendicular Diagonals is a Rhombus

A rhombus is a special kind of parallelogram, in which all the sides are equal. We've seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other. Here we will … [Read more...] about A Parallelogram with Perpendicular Diagonals is a Rhombus

## Heron’s Formula

Today we will use Heron's formula, which is a bit on the long side, but it's very useful. In another post, we saw how to calculate the area of a triangle whose sides were all given, using the fact … [Read more...] about Heron’s Formula

## Area of Rhombus

There are several ways to find the area of a rhombus. A rhombus is a special kind of parallelogram, in which all the sides are equal. Because it is a parallelogram, we can find its area using the … [Read more...] about Area of Rhombus

## Converse of the Pythagorean Theorem

In today's lesson, we will focus on the converse of the Pythagorean Theorem. One of the most useful theorems in Euclidean geometry, which we have used often in other proofs is the Pythagorean … [Read more...] about Converse of the Pythagorean Theorem

## Area of Parallelogram Given Diagonals and a Side

The basic formula for calculating the area of a parallelogram is the length of one side times the height of the parallelogram to that side. But what do we do when we do not have these measurements … [Read more...] about Area of Parallelogram Given Diagonals and a Side

## Circle Inscribed in a Quadrilateral

A tangential quadrilateral is a quadrilateral whose four sides are all tangent to a circle inscribed within it. In such a quadrilateral, the sum of lengths of the two opposite sides of the … [Read more...] about Circle Inscribed in a Quadrilateral