# The median of a trapezoid is always parallel to bases relationship

### | CK Foundation

In a trapezoid, a midline (or a midsegment) is the line joining the midpoints of the sides. In a trapezoid, the midline is parallel to the bases and its length is half. def. A trapezoid is a quadrilateral with at least one pair of parallel sides. THEOREM: The median of a trapezoid is parallel to the bases and half the sum of the. Identify the median of a trapezoid and use its properties. These equal sides are sometimes called the “legs. an isosceles trapezoid will be congruent, but you need to find the relationship between adjacent angles as well.

## Properties of Trapezoids

While most people can memorize these equations and the relationships among the types of mean, most never make the connection to geometry. In this essay, I present seven different types of mean and show how to construct them in a trapezoid. Then I compare their values by constructing all seven types of mean in one trapezoid.

An Introduction to the History of Mathematics.

### Midline in Trapezoid

Arithmetic Mean The arithmetic mean, "A," of any two real numbers "a" and "b" can be found using the following equation: In a trapezoid with bases of lengths "a" and "b," the arithmetic mean, "A," is the length of the segment that is parallel to the bases and that also bisects the sides of the trapezoid.

Click HERE to see a step-by-step construction of the arithmetic mean in a trapezoid. Geometric Mean The geometric mean, "G," of any two real numbers "a" and "b" can be found using the following equation: In a trapezoid with bases of lengths "a" and "b," the geometric mean, "G," is the length of the segment that is parallel to the bases and that also divides the trapezoid into two similar trapezoids.

A trapezoid is a quadrilateral with at least one pair of parallel sides.

## Midline in Trapezoid

The median of a trapezoid is a segment joining the midpoints of the legs of the trapezoid. At the right, is the median for trapezoid ABCD.

The theorems will be stated in "if Both the theorem and its converse where you swap the "if" and "then" expressions will be examined.

Click in the charts below to see each proof. While one method of proof will be shown, other methods are also possible.

**Properties of a Trapezoid-Geometry Help-MooMooMath**

Definition and Theorems pertaining to a trapezoid: The median of a trapezoid is parallel to the bases and half the sum of the lengths of the bases. A isosceles trapezoid is a trapezoid with congruent base angles. Some define a trapezoid as a quadrilateral having only one pair of parallel sides the exclusive definitionthereby excluding parallelograms. The latter definition is consistent with its uses in higher mathematics such as calculus. The former definition would make such concepts as the trapezoidal approximation to a definite integral ill-defined.

### Theorems Dealing with Trapezoids and Kites - MathBitsNotebook(Geo - CCSS Math)

This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid. This is also advocated in the taxonomy of quadrilaterals.

Under the inclusive definition, all parallelograms including rhombusesrectangles and squares are trapezoids. Rectangles have mirror symmetry on mid-edges; rhombuses have mirror symmetry on vertices, while squares have mirror symmetry on both mid-edges and vertices.