12. Which of the following conjectures can be disproved with a counterexample?
    6. The product of any two even integers is even.
    7. The sum of any two prime numbers is even.
    8. Any integer divisible by nine is divisible by three.
    9. The measure of an obtuse angle must be between 90 and 180.

GRIDDED RESPONSE

13. What is the value of x in the figure below?

    

14. In hexagon ABCDEF, ∠ A angle eh  and ∠ B angle b  are right angles. If ∠ C ≅ ∠ D ≅ ∠ E ≅ ∠ F , angle , c approximately equal to , angle , d approximately equal to , angle , e approximately equal to , angle f comma  what is the measure of ∠ F angle f  in degrees?

15. A scale drawing of a swimming pool and deck is shown below. Use the scale 1  in  . = 2 m. 1 , in , . , equals 2 , m.  What is the area of the deck in square meters?

    

16. In parallelogram ABCD below, DB is 15. What is DE?

    

17. The measure of the vertex angle of an isosceles triangle is 112. What is the measure of a base angle?

18. What is the value of x in the figure below?

    

Short Response

19. In rectangle ABCD, A C = 5 ( x − 2 ) eh c equals . 5 open x minus 2 . close  and B D = 3 ( x + 2 ) . b d equals . 3 open x plus 2 . close .  What is the value of x? Justify your answer.
20. Draw line m with point A on it. Construct a line perpendicular to m at A. What steps did you take to perform the construction?
21. Petra visited the Empire State Building, which is approximately 1454 ft tall. She estimates that the scale of the model she bought is 1  in  . = 12  ft  . 1 , in , . , equals 12 , ft , .  Is this scale reasonable? Explain.

Extended Response

22. In the diagram, A B = F E , B C = E D , eh b equals f e comma b c equals e d comma  and A E = F B . eh e equals f b .

    

    1. Is there enough information to prove △ B C G ≅ △ E D G ? white up pointing triangle b c g , approximately equal to white up pointing triangle e d g question mark  Explain.
    2. What one additional piece of information would allow you to prove △ B C D ≅ △ E D C ? white up pointing triangle b c d , approximately equal to white up pointing triangle e d c question mark  Explain.
    3. What can you conclude from the diagram that would help you prove △ B A F ≅ △ E F A ? white up pointing triangle b eh f , approximately equal to white up pointing triangle e f eh question mark
    4. In part (c), is △ B A F ≅ △ E F A white up pointing triangle b eh f , approximately equal to white up pointing triangle e f eh  by SAS or SSS? Explain.

23. At a campground, the 50-yd path from your campsite to the information center forms a right angle with the path from the information center to the lake. The information center is located 30 yd from the bathhouse. How far is your campsite from the lake? Show your work.

    

    Information center

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