Isosceles trapezoid

An isosceles trapezoid ("isosceles trapezium" in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Two opposite sides are parallel, the two other sides are of equal length. The diagonals are of equal length. An isosceles trapezoid's base angles are congruent. Any quadrilateral with one axis of symmetry must be either an isosceles trapezoid or a kite.

Congruent segments

Since segment BC is parallel to segment AD, segment BA is congruent to segment CD. Also, the diagonals of an isosceles trapezoid are congruent and intersect at equal positions. In other words, segment AC and segment BD have equal lengths, segment AE and segment DE are congruent, and segment BE and CE are congruent.

Congruent angles

An isosceles trapezoid has two pairs of congruent angles. The top two would be congruent(same) to one another, and the same for the bottom two angles. Meaning angles EBC and ECB, and angles EAD and EDA.

Area

The area of an isosceles (or any trapezoid) is equal to the average of the bases times the height. In the diagram to the right, "b₁" = segment AD, "b₂" = segment BC and "h" is the length of a line segment between AD and BC and perpendicular to them. The area is given as follows:

$A=frac\{hleft(b\_1+b\_2\; ight)\}\{2\}.$

External links

* [http://www.efunda.com/math/areas/IsosTrapazoid.cfm Some engineering formulas involving isosceles trapezoids]