Lizzy Butler
Kaitlyn Smeraldo
Krisitn Donadio
Definitions
Trapezoid: 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.
•AB and CD are
bases
A
B
•AC and BC are
legs
C
D
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 area
even if you don’t know 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
Trapezoid
Crossword
Helpful Websites
• http://www.mathopenref.com/coordtrapezoid.html
• http://www.coolmath.com/reference/trapezoids.html
• http://www.cliffsnotes.com/study_guide/Trapezoids.to
picArticleId-18851,articleId-18804.html
• http://www.mathwarehouse.com/geometry/quadrilate
rals/trapezoid.php