Lizzy Butler Kaitlyn Smeraldo Krisitn Donadio Trapezoid 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 AC and BC are legs A B 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 length of the bases http://www.mathopenref.com/trapezoidmedian.html

Formulas Area of Trapezoid Perimeter of Regular 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.topicArticleId-18851,articleId-18804.html http://www.mathwarehouse.com/geometry/quadrilaterals/trapezoid.php