Isosceles trapezoid
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Isosceles_trapezoid.jpg
An isosceles trapezoid (isosceles trapezium in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides. This pair of sides is parallel. This makes it automatically a trapezoid. A rectangle is a special case of the isosceles trapezoid, where it doesn't matter which pair of sides you use. Another definition is that an isosceles trapezoid is a trapezoid whose base angles are congruent.
Congruent segments
Since segment BC is parallel to segment AD, segment AB 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.
Isoscelestriangle2.jpg
Congruent angles
Since segment BC is parallel to segment AD, angle ABC is congruent to angle BCD and angle BAD is congruent to angle ADC. Also, angle ABC and angle BAD add up to 180 degrees, as do angles BCD and CDA.
Area
The area of an isosceles trapezoid is equal to the average of the bases times the height, or (b1 + b2) x h ÷ 2; where in the picture above, b1 = segment AD, b2 = segment BC and h is the length of a line perpendicular to segment BC.Template:Geometry-stub