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Trapezoids A quadrilateral that has one set of parallel sides is called a ___________________. For this picture, side AD and side BC (the parallel sides) are called the ________________. Side AB and Side CD are called the ____________. A trapezoid has two sets of __________ angles. In this picture _____ and _____are one set of these, and angles _______ and ________ are the other set. The sum of the interior angles of a trapezoid is ____________. For the picture above, m<a + m<b = ___________, and the m<c +m<d = _________ because when two parallel lines are cut by a transversal, ______________ angles are _________________. If AB = CD in the picture above, then the trapezoid is called an _________ trapezoid. If one of the legs of a trapezoid is perpendicular to both bases, then the trapezoid is called a _______________ trapezoid. 1 Isosceles Trapezoid Suppose you are given isosceles trapezoid ABCD with AB congruent to CD. A line segment drawn with endpoints on each base, that is perpendicular to both bases, is called an _____________ of the trapezoid. In the next picture, two altitudes, AE and CF, will be drawn from base AC to base BD. <AEF, <AEB, <CFD, and <CFE are right angles because of the definition of ______________________. Since < AEF and <CFE are supplementary consecutive angles in quadrilateral ACFE, then AE is ____________to CF. Since AC II EF and AE II CF, then quadrilateral ACFE is a _________________ because of the definition of a parallelogram. Since ACFE is a parallelogram then AE = ______ because the opposite sides of a parallelogram are ___________. (mark on picture above). 2 Now, because of the angles and sides congruent in the picture above, triangle ________ is congruent to ___________ because of the _________ congruence postulate. Since these triangles are congruent, then <B must be congruent to __________ because corresponding parts of congruent triangles are congruent. Also, <BAC and <ACD are going to be congruent. (why) Therefore, in an isosceles trapezoid, we have proven that the base angle pairs of an isosceles triangle are ___________________. Copy theorem 6-14 from Pg. 321 in the textbook below. ______________________________________________________________________ ______________________________________________________________________ . --------------------------------------------------------------------------------------------------------------------- In this isosceles trapezoid, we are going to draw diagonals AD and BC. 3 Notice the two overlapping traingles ABD and CDB. Suppose we draw the two below. AB = CD because of the definition of an _________ trapezoid. BD is equal to BD because of the _____________ property. Furthermore, <ABD is congruent to <CDB because the ________ angles of an isosceles trapezoid are congruent (proved on last page). Mark the congruent parts discussed in the picture above. Triangle ABD≅∆CDB because of the ________congruence postulate. Therefore, AD≅BC because corresponding parts of congruent triangles are congruent. Since AD and BC are the diagonals of the isosceles triangle, this proves that the diagonals of an isosceles triangle are _____________. Copy theorem 6-15 from Pg. 321 below ______________________________________________________________________ ______________________________________________________________________ 4 Medians of a Trapezoid A line that connects the midpoint of the legs of any trapezoid is called the ____________ of the trapezoid. Draw median EF in trapezoid ABCD above. Which two sets of segments would be congruent with each other. __________________ __________________ Theorem 6-16 says the median has two special properties. 1) _____________________________________ 2) _____________________________________ 5 Homework: Pg. 325 # 5-10, 16-28 and guided practice problems on this page #4-24 all 6