1. Ride An amusement park ride has a moving platform attached to four swinging arms. The platform swings back and forth, higher and higher, until it goes over the top and around in a circular motion. In the diagram below, AD and BC represent two of the swinging arms, and DC is parallel to the ground (line l ) . Explain why the moving platform AB is always parallel to the ground.

2. SOLUTION The shape of quadrilateral ABCD changes as the moving platform swings around, but its side lengths do not change. Both pairs of opposite sides are congruent, so ABCD is a parallelogram (why?) 1 4 7 8 2 3 5 6 Your Name Here By the definition of a parallelogram, AB DC . Because DC is parallel to line l , AB is also parallel to line l by the Transitive Property of Parallel Lines. So, the moving platform is parallel to the ground.

3. 1 4 7 8 2 3 5 6 Your Name Here In quadrilateral WXYZ , m W = 42°, m X =138° , m Y = 42° . Find m Z . Is WXYZ a parallelogram? Explain your reasoning. 1. 138°; yes; the sum of the measures of the interior angles in a quadrilateral is 360°, so the measure of is 138°. Since opposite angles of the quadrilateral are congruent , WXYZ is a parallelogram. Z ANSWER

4. The doorway shown is part of a building in England. Over time, the building has leaned sideways. Explain how you know that SV = TU . SOLUTION Since STUV is a parallelogram, SV = TU . Why? 1 4 7 8 2 3 5 6 Your Name Here ARCHITECTURE In the photograph, ST UV and ST UV . What does this tell us? Why?

5. Why is the below a parallelogram? 1 4 7 8 2 3 5 6 Your Name Here 2.

6. Why is the figure below a parallelogram? 1 4 7 8 2 3 5 6 Your Name Here 3.

7. 1 4 7 8 2 3 5 6 Your Name Here Why is the below a parallelogram? 4.

8. SOLUTION AB = distance = CD = 1 4 7 8 2 3 5 6 Your Name Here (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 Show that quadrilateral ABCD is a parallelogram. Slope of AB = Slope of CD =

9. Squares Rhombi h or i Rect angles f or g Parallelograms a or b or c or d e