Assignment: The Quad Squad

1. For this question, you will use your knowledge of quadrilaterals to draw specific shapes that meet each of the following criteria:

A. Draw a parallelogram that is not a square.

B. Draw a quadrilateral that has exactly one pair of parallel sides.

C. Draw a quadrilateral that has perpendicular diagonals.

2. Use the image below to answer problems A-C. Show all work.

A. Calculate the value of x.

B. Calculate the value of MN‾.

C. Calculate the value of NP‾ .

3. EFGH is a kite, with point E on the origin and FG‾= HG‾ = a, where 0 < a < 8. Note FG is parallel to the x-axis and GH is parallel to the y-axis.

A. Give the coordinate of F and H in terms of a. (Hint: Think of the x value of F as 8 minus the value of FG‾ , which is the length a. This might also help you when finding the coordinates of H).

B. Using the coordinate of E, F, G, and H, find the slope of EG‾ and FH‾. Show your work.

C. Use part B to prove that EG‾ ⊥ FH‾.

4. In triangle ABC, Z is the centroid.

Given: AZ‾= 9 and CN‾= 5.5.

A. What does it mean that Z is the centroid and what does it tell us about segments AN‾, BO‾ , and ?

B. Calculate the value of AN‾.

C. Calculate the value of ZN‾ .

D. Calculate the value of CB‾.

5. Given: EFGH is a parallelogram.

A. Calculate the value of x and explain the property of parallelograms that you must know for this problem.

B. Calculate the value of y and explain the property of parallelograms that you must know for this problem.