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.ProblemΔABC 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 … [Read more...] about A parallelogram with Perpendicular Diagonals is a Rhombus

## Heron’s Formula

In another post, we saw how to calculate the area of a triangle whose sides were all given, using the fact that those 3 given sides made up a Pythagorean Triple, and thus the triangle is a right … [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

One of the most useful theorems in Euclidean geometry, which we have used often in other proofs is the Pythagorean Theorem.The Pythagorean Theorem states that in a right triangle, the following … [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

## Consecutive Interior Angles Converse Theorem

The Consecutive Interior Angles Theorem states that the consecutive interior angles on the same side of a transversal line intersecting two parallel lines are supplementary (That is, their sum adds up … [Read more...] about Consecutive Interior Angles Converse Theorem

## A Circle Inscribed in a Square

We've seen that when a square is inscribed in a circle, we can express all the properties of either the square or circle (area, perimeter, circumference, radius, side length) if we know just the … [Read more...] about A Circle Inscribed in a Square

## Square Inscribed in a Circle

When a square is inscribed in a circle, we can derive formulas for all its properties- length of sides, perimeter, area and length of diagonals, using just the circle's radius.Conversely, we can … [Read more...] about Square Inscribed in a Circle