3.6

What If Both Sides Are Parallel?

Pg. 24Properties of Trapezoids

3.6 – What If Both Sides Aren't Parallel?___Propterites 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.

3.33 –FINDING THE AREA OF A TRAPEZOIDA trapezoid: a four-sided shape that has one pair of parallel sides. The sides that are parallel are called bases, as shown in the diagram. Answer the questions below with your team to develop a method to find the area of a trapezoid.

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. Work with a team member to move and rearrange the trapezoid on each piece of tracing paper so that they create a parallelogram.

b1

b2

b1

b2

b. Since you built a parallelogram from two trapezoids, you can use what you know about finding the area of a parallelogram to find the area of the trapezoid. If the bases of each trapezoid are and and the height of each is h, then find the area of the parallelogram. Then use this area to find the area of the original trapezoid.

b1

b2

A(parallelogram) = h(b1 + b2)

1 2

1(trapezoid)

2A h b b

3.34 –AREA OF A TRAPEZOIDCalculate the exact areas of the shapes below. Don't forget units.

32

15

32

A h b b1 2

1

2

A116 20 32

2

A un2416

A h b b1 2

1

2

A18 6 21

2

A un2108

15

A h b b1 2

1

2

A115 9 27

2

A un2270

3.35 –RIGHT TRAPEZOIDSA 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.

givenaddition

Same-side int. are supp.

One pair opp. sides //

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

C B

B C 180

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

3.36 –ISOSCELES TRAPEZOIDSA 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.

A _______B

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

_______D C

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

A _______ 180D

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

B _______ 180C

b. Michael decided to draw in the diagonals of the isosceles trapezoid. Add these lines in below. What do you notice? What other shapes share this property?

Diagonals are congruentLike a rectangle