In this post, we'll take a closer look at a regular hexagon - a six-sided polygon where all the sides are equal. We will look at its angles, and find formulas for its perimeter and area using its side … [Read more...] about Regular Hexagon

## Medians to Legs of a Right Triangle

Here we will use the lengths of the medians to legs of a right triangle to find the length of the hypotenuse and the length of the legs of the triangle. This will also enable us to find the length of … [Read more...] about Medians to Legs of a Right Triangle

## How to Find the Side of a Square From Its Diagonal

A common and easy geometry problem is to find the side of a square from its diagonal. In another problem, we did the opposite - we found the length of the diagonal of a square from its side. We saw … [Read more...] about How to Find the Side of a Square From Its Diagonal

## The Harmonic Mean in a Trapezoid

The harmonic mean is a kind of an average. For two values, a and b, it is defined as H= 2ab/(a+b). So what's the harmonic mean in a trapezoid? We have already seen several lines that are parallel … [Read more...] about The Harmonic Mean in a Trapezoid

## Geometry Word Problems with Distance

Solving geometry word problems is often a challenge. The biggest one is how to translate the description of the problem from words into a graphical representation. In other words, how to visualize the … [Read more...] about Geometry Word Problems with Distance

## Angles of Intersecting Chords

A simple extension of the Inscribed Angle Theorem shows that the measure of the angle of intersecting chords in a circle is equal to half the sum of the measure of the two arcs that the angle and its … [Read more...] about Angles of Intersecting Chords

## Lines that Intersect on a Trapezoid’s Midsegment

A reader wanted some help and sent me the following problem, involving lines that intersect on a trapezoid's midsegment: Problem: EF is the midsegment of trapezoid ABCD, and the two line … [Read more...] about Lines that Intersect on a Trapezoid’s Midsegment

## Converse of the Trapezoid Midsegment Theorem

The Trapezoid Midsegment Theorem states that a line segment connecting the midpoints of the legs of the trapezoid is parallel to the bases, and equal to half their sum. Here, we'll prove the … [Read more...] about Converse of the Trapezoid Midsegment Theorem

## Area of a Trapezoid with Median

In addition to the standard formula for the area of a trapezoid using its bases, we can also calculate the area of a trapezoid with its median and its height. The median is the line connecting the two … [Read more...] about Area of a Trapezoid with Median

## Quadrilateral Whose Diagonals Bisect Each Other

A quadrilateral whose diagonals bisect each other is a parallelogram, as we will show in this exercise. One of the properties of a parallelogram is that its diagonals bisect each other. This is a … [Read more...] about Quadrilateral Whose Diagonals Bisect Each Other