Isosceles trapezoid

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An 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. Also, an isosceles trapezoid's base angles are congruent.

1 Congruent segments
2 Congruent angles
3 Area
4 External links

[edit] 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.

Another isosceles trapezoid.

[edit] Congruent angles

An isosceles trapezoid has two pairs of congruent angles. The top two would be congruent to one another, and the same for the bottom two angles.

[edit] Area

The area of an isosceles trapezoid (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:

$A=\frac{h\left(b_1+b_2\right)}{2}$