A Trapezoid With Congruent Legs
Trapezoid
A trapezoid is a quadrilateral with one pair of parallel sides. The figure below shows a few different types of trapezoids.
Note: Some define a trapezoid as a quadrilateral with at least i pair of parallel sides implying that it could contain two pairs of parallel sides, which would make information technology a parallelogram. For the sake of this commodity, we will define a trapezoid as a quadrilateral with simply one pair of parallel sides.
Sides of a trapezoid
The parallel sides of a trapezoid are referred to every bit its bases. The non-parallel sides are called legs. The height (or altitude) is the line segment used to mensurate the shortest altitude between the 2 bases.
Angles of a trapezoid
In a trapezoid, the pair of angles that share a mutual base of operations are called base angles. For the trapezoids shown in the diagram beneath, ∠A and ∠D are base angles and ∠B and ∠C are base angles. The pair of angles next to a leg are supplementary: ∠A + ∠B = 180° and ∠C + ∠D = 180°.
Midsegment of a trapezoid
The midsegment of a trapezoid is a line segment connecting the midpoint of its legs. A midsegment is parallel to the bases and has a length that is one-half the sum of the two bases.
In the effigy higher up, midsegment divides legs AB and CD in half and 
Area of a trapezoid
The area, A, of a trapezoid is one-half the product of the sum of its bases and its height.
where h is the height and b1 and b2 are the base lengths.
Trapezoid classifications
Trapezoids tin exist classified as scalene or isosceles based on the length of its legs. If the legs and base of operations angles of a trapezoid are congruent, information technology is an isosceles trapezoid. Otherwise, it is a scalene trapezoid.
| Scalene trapezoid | Isosceles trapezoid |
|---|---|
 |  |
| Legs or base angles non congruent | Congruent legs and base angles |
Trapezoids tin can also be classified as right trapezoids or birdbrained trapezoids based on its angles. If 1 of the legs is perpendicular to the bases, the trapezoid is a correct trapezoid. Otherwise the trapezoid must comprise two obtuse angles and is called an obtuse trapezoid.
| Correct trapezoid | Obtuse trapezoid |
|---|---|
 | |
| I leg is perpendicular to the bases. | 2 angles are obtuse. |
Isosceles trapezoids
An isosceles trapezoid is a special trapezoid with coinciding legs and base angles. It has the following properties.
A Trapezoid With Congruent Legs,
Source: https://www.math.net/trapezoid
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