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6.3 What If Both Sides Are Parallel? Pg. 13 Properties of Trapezoids

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6.3 – What If Both Sides Aren't Parallel?___ Properties of Trapezoids In the previous lesson, you learned that parallelograms have both pairs of opposite sides parallel. Today you will study a shape that has only one pair of opposite sides parallel.

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Trapezoid: Quadrilateral with one pair of parallel sides

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a. Saundra noticed that two identical trapezoids can be arranged to form a parallelogram. Trace the trapezoid shown below onto a piece of tracing paper. Be sure to label its bases and height as shown in the diagram. Then determine a formula to find the area of the original trapezoid.

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b1b1 b2b2

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b1b1 b2b2 A(parallelogram) = h(b 1 + b 2 )

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Trapezoid

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6.15 –AREA OF A TRAPEZOID Calculate the exact areas of the trapezoids below. Don't forget units. 32

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x 2 + 6 2 = 10 2 x 2 + 36 = 100 x 2 = 64 x = 8 8

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1423 O A 20.71

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6.16 –RIGHT TRAPEZOIDS A quadrilateral with two consecutive right angles is called a right trapezoid.

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a. If two consecutive angles are 90°, does it have to be a trapezoid? How do you know? Explain using the proof below.

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given addition Consecutive int. are supp. One pair opp. sides //

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b. What do you know about and now that you know that ABCD is a trapezoid?

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c. What if the angles were not consecutive? Does it still have to be a trapezoid? Draw a picture to support your answer. No. The angles have to be consecutive

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6.17 –ISOSCELES TRAPEZOIDS A trapezoid with its legs congruent is called isosceles.

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a. Using reflection symmetry, what can you say about the angles in the picture? Complete the statements.

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b. Complete the two new properties of isosceles trapezoids.

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Isosceles Trapezoid: Base angles are congruent Diagonals are congruent

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6.18 –MISSING ANGLES Find the measure of the missing angles in the isosceles trapezoids.

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6.19 –TRAPEZOIDS ON THE GRID Prove the following shape is a trapezoid. Then prove it isn’t isosceles.

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Slopes of: AB = BC = CD = DA =

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Lengths of: AB = BC = CD = DA =

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Midsegment of a Trapezoid: Connects the midpoints of the legs of a trapezoid midsegment base midsegment = base + base 2

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x = 7 + 13 2 = 20 2 = 10 6.20 –TRAPEZOIDS ON THE GRID Find x. x

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M = b + b 2 20 = 7x +12 2 1 7x + 12 = 40 x = 4 7x = 28 12

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Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Kite Triangle

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Trapezoid

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One pair of parallel sides Consecutive angles supplementary

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Isosceles Trapezoid

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Properties listed above Legs are congruent Base angles congruent Diagonals are congruent

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