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

# Trapezoids

A quadrangle in which one pair of opposite sides are parallel to each other, but the other pair is not, is called a trapezoid.

Outside of the US and Canada, it is often called a trapezium.

Trapezoids are usually drawn with one of the parallel edges at the bottom. The parallel edges are called the bases, while the non-parallel edges are called the sides.

There are several types of special trapezoids.

"Right trapezoids" have one side which is perpendicular to the bases, creating two right angles.

Isosceles trapezoids have two sides which are equal sized and have the same angles between themselves and the bases.

--

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

## 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

## Similar Trapezoids

In today's lesson, we will find a formula for the length of a line parallel to the bases of a trapezoid that splits it into two similar trapezoids. We have looked at a couple of special lines … [Read more...] about Similar Trapezoids

## Line Parallel to the Base of a Trapezoid

There are a number of interesting features of lines drawn parallel to the bases of a trapezoid. We saw one of these in this problem- a line parallel to the bases and connecting the midpoints of the … [Read more...] about Line Parallel to the Base of a Trapezoid

## Trapezoid Midsegment Theorem

In today's geometry lesson, we will prove the trapezoid midsegment theorem, relying on the previously proven triangle midsegment theorem. The triangle midsegment theorem states that the line … [Read more...] about Trapezoid Midsegment Theorem

## Trapezoids: Adjacent angles are Supplementary

In a trapezoid, the two angles that are on the same leg (one on the top base, one on the bottom base) are called 'adjacent angles'. These adjacent angles are supplementary, which means their measures … [Read more...] about Trapezoids: Adjacent angles are Supplementary