Name: ________________________ Class: ___________________ Date: __________ ID: A

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Geometry Semester 2 Exam Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

Identify the congruent triangles in the figure.

____ 1.

a. ∆KLJ ≅ ∆ONM c. ∆LJK ≅ ∆OMNb. ∆KJL ≅ ∆OMN d. ∆JKL ≅ ∆ONM

Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.

____ 2. 3, 9, 10a. Yes; the third side is the longest.b. No; the sum of the lengths of two sides is not greater than the third.c. No; the first side is not long enough.d. Yes; the sum of the lengths of any two sides is greater than the third.

Short Answer

Find the measures of the sides of ∆ABC and classify the triangle by its sides.

3. A 5,− 2ÊËÁÁ ˆ

¯˜̃ ,B 7, 2Ê

ËÁÁ ˆ

¯˜̃ ,C 3, 5Ê

ËÁÁ ˆ

¯˜̃

Find each measure.

4. m∠1, m∠2, m∠3

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Name the congruent angles and sides for the pair of congruent triangles.

5. ∆SKL ≅ ∆CFG

Refer to the figure. ∆ARM, ∆MAX, and∆XFM are all isosceles triangles.

6. What is m∠RAM ?

7. If m∠FXA = 96, what is m∠FXM ?

8. Triangle FJH is an equilateral triangle. Find x and y.

9. Triangle RSU is an equilateral triangle. RT bisects US . Find x and y.

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10. Lines s, t, and u are perpendicular bisectors of the sides of ∆FGH and meet at J. If JG = 4x + 3, JH = 2y − 3, JF = 7 and HI = 3z − 4, find x, y, and z.

11. ZC is an altitude, ∠CYW = 9x + 38, and ∠WZC = 17x. Find m∠WZC.

Determine the relationship between the lengths of the given sides.

12. ZX , YX

13. Find the measure of each interior angle for a regular pentagon. Round to the nearest tenth if necessary.

14. Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary.

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Complete the statement about parallelogram ABCD.

15. ∠CDA ≅

Determine whether the quadrilateral is a parallelogram. Justify your answer.

16.

Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.

17. A(1, − 6), B(−1,− 3), C(−2, 7), D(0, 4); Slope Formula

Quadrilateral ABCD is a rectangle.

18. If AG = −4k + 24 and DG = 9k + 102, find BD.

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19. In rhombus YZAB, if YZ =12, find AB.

Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. List all that apply.

20. A(5, 10), B(4, 10), C(4, 9), D(5, 9)

21. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.

22. For trapezoid JKLM, A and B are midpoints of the legs. Find AB.

23. Find the geometric mean between each pair of numbers.28 and 7

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24. Find the measure of the BD.

25. Find x.

26. Find x and y.

27. Find x and y.

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28. Find the measure of the angle to the nearest tenth of a degree.cosY = 0.5135

29. Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1472 feet. Find his distance from the Empire State Building to the nearest foot.

30. A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5° for the next 40 ground miles. About how far above sea level is the rocket ship after its climb?

31. A hiker stops to rest and sees a deer in the distance. If the hiker is 48 yards lower than the deer and the angle of elevation from the hiker to the deer is 15°, find the distance from the hiker to the deer.

Find each measure using the given measures of ∆KLM . Round measures to the nearest tenth.

32. If m∠L = 48.4, m∠K = 24.5, and l = 37.9, find k.

The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest hundredth if necessary.

33. r = 13.1 km, d = ? , C = ?

34. Find the exact circumference of the circle.

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Use the diagram to find the measure of the given angle.

35. m∠BAC

36. m∠CAE

37. In ñO, EC and AB are diameters, and ∠BOD ≅ ∠DOE ≅ ∠EOF ≅ ∠FOA.

Find m arc BC.

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38. In ñU , TS = 15, UQ = US. Find mPR.

39. Find x. Assume that segments that appear tangent are tangent.

Find the measure of the numbered angle.

40.

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Find x. Assume that any segment that appears to be tangent is tangent.

41.

42. Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.

43. Find the area of the figure. Round to the nearest tenth if necessary.

44. Find the area of the figure. Round to the nearest tenth if necessary.

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45. Find the area of the figure. Round to the nearest tenth if necessary.

46. Find the area of a circle having a circumference of 34π. Round to the nearest tenth. Use 3.14 for pi.

Find the area of the figure. Round to the nearest tenth if necessary.

47.

48.

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Find the lateral area of each prism. Round to the nearest tenth if necessary.

49. The dimension labeled 10 is the height of the prism.

50.

Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer.

51.

52.

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Find the surface area of the cylinder. Use 3.14 for pi and round your answer to the nearest tenth.

53.

Find the surface area of the regular pyramid. Round to the nearest tenth if necessary.

54.

Find the volume of the prism. Round to the nearest tenth if necessary.

55.

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Find the volume of the cone. Use 3.14 for π. Round to the nearest tenth.

56.

57. Baseballs and softballs come in different sizes for different types of leagues. If the diameter of a baseball is 3 inches and a softball has a diameter of 3.8 inches, find the difference between the volumes of the two balls. Use 3.14 for π. Round to the nearest tenth.

Write a two-column proof.

58. Given: R is the midpoint of SU ; SV ≅ UV .Prove: ∆RSV ≅ ∆RUV

59. If FG ⊥ IJ and IG ≅ JG, then FI ≅ FJ .

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60. A triangle is formed by three kitchen appliances as shown in the figure. The distances shown are measured in feet. What is wrong with the labels on the triangle?

Essay

61. The vertices of a triangle are L 1,3ÊËÁÁ ˆ

¯˜̃ , M 4,0Ê

ËÁÁ ˆ

¯˜̃ , N −4,1Ê

ËÁÁ ˆ

¯˜̃ .

a. Graph the triangle.b. Use the Distance Formula to find the length of each side to the nearest tenth.

c. LO is a median of the triangle. What are the coordinates of point O? Explain.

d. Graph median LO.