Geometry Benchmark Name: ________________________________________________#5 Review Date : _________________________ Per: __________

1. Given: aPb . What is the m1 and m2 ? Which transversal rules did you use?

2. Given: AB PCD . What is the m1 and m2 ? Which transversal rules did you use?

3. Given the figure below, find the relationship and type of measurement (congruent or supplementary) between the angles given.

a) angle 5 and angle 7:

b) angle 6 and angle 3:

c) angle 1 and angle 8:

d) angle 2 and angle 3:

e) angle 4 and angle 7:

f) angle 1 and angle 5:

g) angle 6 and angle 8:

4. Given the figure below andm147 . Name the angle size, and the angle relationship that helped you find the angle size.

a) m2

b) m7

c) m3

d) m5

e) m6

f) m4

5. When working with parallel lines and transversals, what conclusions can you draw about obtuse and acute angles?

6. Suppose you have a triangle with side lengths 28, 45, and 53. Is it a right triangle? If not what kind of triangle is it?

1

7. A 16-foot ladder is leaned against a wall. If the base of the ladder is 6 feet from the wall, how high up on the wall does the ladder reach?

8. Mr. Thomas just bought a big-screen TV set. The screen is 48 inches wide and 36 inches high. Find the length of its diagonal.

9. What kind of triangle is formed if it has the side lengths of 4, 5, and 7?

10. Suppose you have a triangle with side lengths 28, 20, and 21. Is it a right triangle? If not, what type of triangle is it?

11. Find the measure of the missing side. 12. Find the missing side length, if possible.

13. Find mABC andmCBD . 14. FindA ,B , and C .

2

15. In the picture below, CAT TCA and1123 .

a. Find mATC using triangle sum theorem.

b. Find mATC using exterior angle theorem.

16. Name the 4 area formulas we talked about in class.a. Square: b. Rectangle:

c. Triangle: d. Circle:

17. Name the 5 volume formulas we learned.

a. Cube: b. Rectangular Prism:

c. Cylinder: d. Cone:

e. Sphere:

18. A candle maker uses a cylinder mold, which is 14 inches tall and has a radius of 1.5 inches. What is the volume of the candle mold?

19. Which will carry the most water: two pipes, one with a 6 cm radius and the other with a 8 cm radius, or a pipe with a 9 cm radius? (Assume all heights are the same) Show work. Explain.

20. Find the volume of the sphere shown below. Give your answer in pi and decimal form. Round to the nearest 10th.

3

21. Find the volume of an ice cream cone, with one scoop of ice cream. If the radius of both the cone, and the ice cream (sphere) is 6 cm, and the height of the cone is 9 cm.

22. A cylindrical glass 4 in. in diameter and 8 in tall is filled with water to a height of 6 in. If a ball 3 in. in diameter is dropped into the glass and sinks to the bottom, will the water in the class overflow? Explain and justify your response.

23. Find the perimeter and area of the base, as well as the volume of the figure shown below.

24. Find the circumference and area of the base, and the volume of the figure shown below.

25. Find the volume of the figure below. Give your answer in pi form and decimal form, round to the nearest 10th.

4