14. Which is the most valid conclusion based on the statements below?

    If a triangle is equilateral, then it is isosceles. Δ A B C cap delta eh b c  is not equilateral.

    6. Δ ABC cap delta  is not isosceles.
    7. Δ ABC cap delta  is isosceles.
    8. Δ ABC cap delta  may or may not be isosceles.
    9. Δ ABC cap delta  is equilateral.

GRIDDED RESPONSE

15. What is m ∠ 1 m angle 1  in the figure below?

    
    Image Long Description

16. ∠ ABE angle  and ∠ CBD angle  are vertical angles and both are complementary with ∠ FGH . angle  If m ∠ ABE = ( 3 x − 1 ) , m angle  and m ∠ FGH = 4 x , m angle  what is m ∠ CBD ? m angle

17. What is the value of x in the kite below?

    

18. A 3-ft-wide walkway is placed around an animal exhibit at the zoo. The exhibit is rectangular in shape and has length 15 ft and width 8 ft. What is the area, in square feet, of the walkway around the exhibit?

19. The outer walls of the Pentagon in Arlington, Virginia, are formed by two regular pentagons, as shown below. What is the value of x?

    

Short Response

20. What are the possible values for n to make ABC a valid triangle? Show your work.

    

21. The pattern of a soccer ball contains regular hexagons and regular pentagons. The figure below shows what a section of the pattern would look like on a flat surface. Use the fact that there are 360 ° 360 degrees  in a circle to explain why there are gaps between the hexagons.

    

Extended Response

22. A parallelogram has vertices L ( − 2 , 5 ) , l open negative 2 comma 5 close comma  M(3, 3), and N(1, 0). What are possible coordinates for its fourth vertex? Explain.

23. Jim is clearing out trees and planting grass to enlarge his backyard. He plans to double both the width and the length of his current rectangular backyard, as shown below.

    

    1. How will the area of Jim's new backyard compare to the area of his current backyard?
    2. Will it take Jim twice as long to mow his new backyard than his old backyard? Explain. (Assume Jim mows at the same rate for both yards.)

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