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Module 7 Lesson 4 Trapezoids and Kites Remediation Notes Slide 1: “A trapezoid cannot have both pairs of opposite sides parallel. As you can see here, we have two bases that are parallel, but our legs are not parallel. So, the parallel sides are called bases and the non parallel sides are called legs. A trapezoid actually has two pairs of base angles. C and D are one pair of base angles; A and B are the second pair of base angles.” Slide 2: “If the angles are adjacent but not base angles – here D and C are base angles, but we want to talk about D and A – then they are supplementary. Again, A and B are base angles, but if we talk about B and C, we know that they are supplementary.” Slide 3: “We do have special trapezoids; isosceles is a special trapezoid. If the two sides that are not parallel are the same length, then it’s an isosceles trapezoid. This means as it does in an isosceles triangle that those base angles that are opposite the sides are congruent. A trapezoid is isosceles if and only if its diagonals are congruent. So, if you can imagine two diagonals in here, they would have to be congruent.” Slide 4: No words. Slide 5: “The midsegment of a trapezoid is parallel to each base. So, segment AD is parallel to the midsegment is parallel to segment BC. The midsegment is also half the sums of the lengths of the bases. That means that if I add the measure of AD to the measure of BC, I get a value, and if I divide that by two, I get the measure of my midsegment.” Slide 6: “When we look at kites, we see that a kite is quite different from most of our parallelograms. First of all, we have two pairs of consecutive congruent sides. Up here we have one pair of consecutive congruent sides, and down here we have another pair of consecutive congruent sides. However, opposite sides are not congruent in a kite. These are opposite sides and they are not congruent.” Slide 7: “We also know that the diagonals of a kite are perpendicular.” Slide 8: “Finally, if a quadrilateral is a kite, then we have exactly one pair of opposite angles that are congruent. So, that means that angle A and angle C are congruent, and angle B and angle D are congruent.”