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

## Angle bisector is perpendicular to the base in an isosceles triangle

In another problem, we saw that in an isosceles triangle, the height to the base from the apex is also the angle bisector. Here, we will show the opposite: that the angle bisector is perpendicular to … [Read more...] about Angle bisector is perpendicular to the base in an isosceles triangle

## Quadrilateral Formed by Joining Midpoints of Rhombus

What is the shape of the quadrilateral formed by joining the midpoints of a rhombus? In an earlier post, we saw that the quadrilateral formed by joining midpoints of any quadrilateral is a … [Read more...] about Quadrilateral Formed by Joining Midpoints of Rhombus

## Quadrilateral Formed by Joining Midpoints of a Rectangle

If joining the midpoint of a rhombus forms a rectangle, what is the shape of the quadrilateral formed by joining midpoints of a rectangle? If you guessed it is a rhombus, you are correct, as we will … [Read more...] about Quadrilateral Formed by Joining Midpoints of a Rectangle

## Parallel Lines are Equidistant

"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