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Trapezoid

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

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Trapezoid

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  1. Trapezoid Lizzy Butler Kaitlyn Smeraldo Krisitn Donadio

  2. 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)

  3. 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

  4. Properties of Isosceles Trapezoids • Angles: • The angles on either side of the bases are congruent • Adjacent angles along the legs are supplementary

  5. …Continued Isosceles • Diagonals: • The diagonals are congruent only for isosceles trapezoids

  6. …Continued Isosceles • Sides: • The bases are parallel, as in all trapezoids • By definition, the opposite sides are congruent

  7. 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 Lines of Symmetry

  8. 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

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

  10. 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

  11. 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

  12. TrapezoidCrossword

  13. 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

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