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DefinitionsTrapezoid: quadrilateral that has only two parallel sides

Isosceles Trapezoid: A trapezoid in which the non-parallel sides are congruent

Scalene Trapezoid: A trapezoid in which the non-parallel sides are not congruent

Right Trapezoid: A trapezoid in which one of the non-parallel sides is perpendicular to the two parallel sides (forming two right angles)

Sides of trapezoids• The two parallel sides are called bases.• The two non-parallel sides (regardless if

congruent) are called legs.

A B

C D

•AB and CD are bases

•AC and BC are legs

Properties of Isosceles Trapezoids

• Angles:– The angles on either side of the bases are

congruent– Adjacent angles along the legs are supplementary

…Continued Isosceles

• Diagonals:– The diagonals are congruent only for isosceles

trapezoids

…Continued Isosceles

• Sides:– The bases are parallel, as in all trapezoids– By definition, the opposite sides are congruent

Lines of Symmetry

• In an isosceles trapezoid, a line of symmetry can be drawn from the midpoint of Base 1 to the midpoint of Base 2.– Is perpendicular to the midsegment of a trapezoid

• There are no lines of symmetry present in a scalene trapezoid and a right trapezoid.– Scalene: all sides are different lengths and therefore cannot

be symmetrical on any sides– Right: one side of a trapezoid is straight and the other is on

a diagonal, so a symmetrical line can not be constructed

Coordinate Geometry

• The Bases will exhibit the same slope• Legs

– Isosceles trapezoid: legs will have same distance (length)– Right trapezoid: one leg will have an undefined slope and

the other leg will be an oblique line; distances are different

– Scalene trapezoid: both legs will have different slope and distance

http://www.mathopen%ref.com/coordtrapezoid.html

Coordinate Geometry

• If you know the coordinates of the four vertices, you can find different properties of the trapezoid, including area and perimeter.

The Median

• Joins the midpoints of its legs• Special relationship to bases

– Theorem: The median of a trapezoid is parallel to both bases, and its measure is one-half the sum of the measures of the bases (average of bases)

• M= ½ (b1 + b2)

• Length of median can be used to find the length of the bases

http://www.mathopenref.com/trapezoidmedian.html

Formulas

• Area of Trapezoid– A= ½ h (b1 + b2)

– A= Altitude x median– Originates from parallelogram (2 trapezoids, one

right side up, one down)• Area of Parallelogram= b x h

• Perimeter of Regular Trapezoid– P= a + b1 + c + b2

TrapezoidCrossword

Helpful Websites

• http://www.mathopenref.com/coordtrapezoid.html• http://www.coolmath.com/reference/trapezoids.html• http://www.cliffsnotes.com/study_guide/

Trapezoids.topicArticleId-18851,articleId-18804.html• http://www.mathwarehouse.com/geometry/

quadrilaterals/trapezoid.php