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

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Presentation transcript:

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

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.

Trapezoid: Quadrilateral with one pair of parallel sides

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.

b1b1 b2b2

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

Trapezoid

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

x = 10 2 x = 100 x 2 = 64 x = 8 8

1423 O A 20.71

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

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

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

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

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

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

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

b. Complete the two new properties of isosceles trapezoids.

Isosceles Trapezoid: Base angles are congruent Diagonals are congruent

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

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

Slopes of: AB = BC = CD = DA =

Lengths of: AB = BC = CD = DA =

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

x = = 20 2 = –TRAPEZOIDS ON THE GRID Find x. x

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

Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Kite Triangle

Trapezoid

One pair of parallel sides Consecutive angles supplementary

Isosceles Trapezoid

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