By the Trapezoid Diagonals Theorem, the diagonals of an isosceles trapezoid are congruent. Based on the definition of a trapezoid, it is a quadrilateral with at least one pair of parallel sides. A trapezoid will not always have congruent bases. By its definition, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. By definition of a rhombus, it is a quadrilateral with four equal-length sides and opposite sides parallel to each other. Based on the definition of an isosceles trapezoid, it is a trapezoid in which both legs and both base angles are of the same measure. Reflecting isosceles trapezoid ABCE across FE preserves it, making FE a line of symmetry. In the figure above, altitude FE bisects bases AD and BC.

$the legs of an isosceles trapezoid are$

An isosceles trapezoid has one line of symmetry: the altitude that bisects its bases.

In the diagram above, AE = DE, BE = CE, and

The ratio of the segments making up the diagonals of a trapezoid are proportional.

Since the legs of an isosceles trapezoid are congruent and the following pairs of triangles share a base, в–іABD в‰… в–іDCA and в–іABC в‰… в–іDCB by the Side-Side-Side postulate. In the isosceles trapezoid below, diagonals AC and BD are congruent.

The two diagonals of an isosceles trapezoid are congruent.

Right trapezoidДЄn isosceles trapezoid is a special trapezoid with congruent legs and base angles. Otherwise the trapezoid must contain two obtuse angles and is called an obtuse trapezoid. If one of the legs is perpendicular to the bases, the trapezoid is a right trapezoid. Trapezoids can also be classified as right trapezoids or obtuse trapezoids based on its angles. If the legs and base angles of a trapezoid are congruent, it is an isosceles trapezoid. Trapezoids can be classified as scalene or isosceles based on the length of its legs. Where h is the height and b 1 and b 2 are the base lengths. The area, A, of a trapezoid is one-half the product of the sum of its bases and its height.

In the figure above, midsegment EF divides legs AB and CD in half and Area of a trapezoid A midsegment is parallel to the bases and has a length that is one-half the sum of the two bases. The midsegment of a trapezoid is a line segment connecting the midpoint of its legs. The pair of angles next to a leg are supplementary: в€ A + в€ B = 180В° and в€ C + в€ D = 180В°. For the trapezoids shown in the diagram below, в€ A and в€ D are base angles and в€ B and в€ C are base angles. In a trapezoid, the pair of angles that share a common base are called base angles. The height (or altitude) is the line segment used to measure the shortest distance between the two bases. The parallel sides of a trapezoid are referred to as its bases. For the sake of this article, we will define a trapezoid as a quadrilateral with only one pair of parallel sides. Note: Some define a trapezoid as a quadrilateral with at least one pair of parallel sides implying that it could contain two pairs of parallel sides, which would make it a parallelogram. The figure below shows a few different types of trapezoids. Home / geometry / shape / trapezoid TrapezoidДЄ trapezoid is a quadrilateral with one pair of parallel sides.

The legs of an isosceles trapezoid are