Isosceles trapezoid. Ratios of some segments in an isosceles trapezoid.

Isosceles trapezoid. Ratios of some segments in an isosceles trapezoid. The property of a trapezoid with mutually perpendicular diagonals.

If in a quadrilateral (ABCD), two sides are parallel and the other are not parallel but equal, is called an isosceles trapezoid.

The isosceles trapezoid is also recognized by the following signs:

If the angles at the bases are equal:
If the diagonals are equal:
If the sum of the opposite angles equals 180 °:
The segment drawn through the midpoints of the sides is called the midline (m).

And the segments connecting the vertices of the non-adjacent corners of the trapezoid were called diagonals.

Trapezium has a number of properties:

If a circle can be inscribed into an isosceles trapezoid, then the lateral side is equal to the midline of the trapezoid: AB = CD = m. (m = (AD + BC) / 2.
A circle can be described around an isosceles trapezoid.
If the diagonals of the trapezoid are mutually perpendicular, then the height (h) is equal to the center line of the trapezoid, h = m.
If the diagonals are mutually perpendicular, then the area of ​​the trapezoid is equal to the square of the height: SABCD = h2.
If a circle can be inscribed into an isosceles trapezoid, then the square of the height is equal to the product of the bases of the trapezoid: h2 = BC * AD.
The sum of the squares of the diagonals is equal to the sum of the squares of the sides plus twice the product of the trapezoid bases: AC ^ 2 + BD ^ 2 = AB ^ 2 + CD ^ 2 + 2BC * AD.