GRIDDED RESPONSE

11. A triangle has a perimeter of 81 in. If you divide the length of each side by 3, what is the perimeter, in inches, of the new triangle?
12. A jewelry maker designed a pendant like the one shown below. It is a regular octagon set in a circle. Opposite vertices are connected by line segments. What is the measure of angle P in degrees?

    

13. The diagonal of a rectangular patio makes a 70 ° 70 degrees  angle with a side of the patio that is 60 ft long. What is the area, to the nearest square foot, of the patio?
14. What is the area, in square feet, of the unshaded part of the rectangle below?

    

15. You are making a scale model of a building. The front of the actual building is 60 ft wide and 100 ft tall. The front of your model is 3 ft wide and 5 ft tall. What is the scale factor of the reduction?
16. At 8 o'clock, what is the measure, in degrees, of the angle formed by the two hands of the clock?

    

17. A square has an area of 225   cm 2 . 225 , cm squared , .  If you double the length of each side, what is the area, in square centimeters, of the new square?

Short Response

18. Use a compass and straightedge to copy the diagram of the circle below. Label the center, radius, and diameter. Then label a central angle, an arc, a sector, and a segment.

    

19. The coordinates of Δ A B C cap delta eh b c  are A(2, 3), B(10, 9), and C ( 10 , − 3 ) . c open 10 comma negative 3 close .  Is Δ A B C cap delta eh b c  an equilateral triangle? Explain.
20. Draw a right triangle. Then construct a second triangle congruent to the first. Show your steps.
21. One diagonal of a parallelogram has endpoints at P ( − 2 , 5 ) p open negative 2 comma 5 close  and R ( 1 , − 1 ) . r open 1 comma negative 1 close .  The other diagonal has endpoints at Q(1, 5) and S ( − 2 , − 1 ) . s open negative 2 comma . negative 1 close .  What type of parallelogram is PQRS? Explain.

Extended Response

22. The coordinates of the vertices of isosceles trapezoid ABCD are A(0, 0), B(6, 8), C(10, 8), and D(16, 0). The coordinates of the vertices of isosceles trapezoid AFGH are A(0, 0), F(3, 4), G(5, 4), and H(8, 0). Are the two trapezoids similar? Justify your answer.

23. The circle graph below shows fall sports participation at one school.

    

    Fall Sports Participation

    1. How many degrees greater is the measure of the angle that represents soccer than the measure of the angle that represents cross-country? Show your work.
    2. If 48 students play soccer, how many run cross-country? Explain your reasoning.

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