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Encyclopedia > Isosceles trapezoid
An isosceles trapezoid and its axis of symmetry.
An isosceles trapezoid and its axis of symmetry.

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. Two opposite sides are parallel, the two other sides are of equal length. The diagonals are of equal length. An isosceles trapezoid's base angles are congruent. This article is about the geometric figure. ... British English (BrE, BE, en-GB) is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere in the Anglophone world. ... This article is about the geometric shape. ... Sphere symmetry group o. ... This article is about the geometric figure. ... Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ... An example of congruence. ...

Contents

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. A diagonal can refer to a line joining two nonadjacent vertices of a polygon or polyhedron, or in contexts any upward or downward sloping line. ... See also: congruence relation In geometry, two shapes are called congruent if one can be transformed into the other by a series of translations, rotations and reflections. ...

Another isosceles trapezoid.
Another isosceles trapezoid.

Image File history File linksMetadata Isoscelestriangle2. ... Image File history File linksMetadata Isoscelestriangle2. ...

Congruent angles

An isosceles trapezoid has two pairs of congruent angles. The top two would be congruent(same) to one another, and the same for the bottom two angles. Meaning angles EBC and ECB, and angles EAD and EDA.


Area

The area of an isosceles (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{hleft(b_1+b_2right)}{2}


External links

  • Some engineering formulas involving isosceles trapezoids

  Results from FactBites:
 
Untitled Document (576 words)
A trapezoid is a quadrilateral with at least one pair of parallel sides by one definition and by another a trapezoid has exactly one pair of parallel sides.
The portion of the median contained between the diagonals of a trapezoid is equal in length to the difference between the bases of the trapezoid.
The diagonals of an isosceles trapezoid are congruent.
Trapezoid - MSN Encarta (104 words)
Trapezoid, in plane geometry, quadrilateral (four-sided) figure with two parallel sides, or bases, of unequal length.
The sides that are not parallel are called legs, and a line from the midpoint of one leg to the midpoint of the other is called the median; the multiplication of the altitude and the median yields the area of the trapezoid.
When the legs of a trapezoid are of equal length, the figure is called an isosceles trapezoid.
  More results at FactBites »


 

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