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Trapezoids Dapo Adegbile Brandon Abad Jude St. Jean Period:12 Definition A quadrilateral that has 1 pair of parallel sides A trapezoid with 1 pair of congruent sides Properties of sides The bases (top and bottom) of an isosceles trapezoid are parallel. The legs of an isosceles trapezoid are congruent. The angles on either side of the bases are congruent. The bases (top and bottom) of a trapezoid are parallel. Unlike the Isosceles Trapezoid it does not need to have any congruent sides. Properties of angles Adjacent angles along the sides are supplementary. Base angles of isosceles trapezoid are congruent. Normal trapezoids don’t have any special properties. All of the angles within a trapezoid add up to 360 degrees. Proof Given: BC ll AD, AB = DC Prove: <1=<2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Quad. ABCD is an Isosceles Trapezoid BC ll AD AB = DC Construct a line through C that is ll to AB AB ll EC Quad ABCE is a parallelogram AB = EC DC = CE <3 = <4 <1 = <3 <1 = <4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Given Given Given Construction Construction Definition of a parallelogram Opposite sides of Parallelogram are congruent Transitive Property Isosceles Triangle Theorem (if sides than angles) Corresponding angles Transitive property Properties of diagonals The diagonals of an isosceles triangle are congruent. Nothing special happens with the diagonals. Proof Given: PQRS is an Isosceles Trapezoid SR ll PQ SP=RQ Prove: RP=SQ 1. 2. 3. 4. 5. 6. Quad. PQRS is a trapezoid SR ll PQ SP=RQ <SPQ=<RPQ PQ=PQ RP=SQ 1. 2. 3. 4. 5. 6. Given Given Given Definition of Trapezoid Reflexive Property CPCTC Lines of symmetry A regular trapezoid has no lines of symmetry Isosceles trapezoids have only 1 line of symmetry Coordinate Geometry http://mathopenref.com/coordtrapezoid.html formulas Perimeter = a + b + c + B Area = 1/2h(B+b) Area of parallelogram (B+b) x h But, this is double of what we need. So, multiply by 1/2. The Area could also be altitude x median Other facts Right Trapezoid- a trapezoid with 2 right angles median- is a line segment linking the midpoints of the two legs of the trapezoid To find the length of the median you can find the length of the base and divide it by 2 or find the distance between the 2 midpoints of the legs Altitude- is the perpendicular distance from one base to the other British call it Trapezium Suggested Websites http://mathopenref.com/coordtrapezoi d.html http://www.coolmath.com/reference/tr apezoids.html http://www.cliffsnotes.com/study_guid e/Properties-ofTrapezoids.topicArticleId18851,articleId-18798.html