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Name: ________________________ Class: ___________________ Date: __________<br />
ID: A<br />
Geometry <strong>Semester</strong> 2 <strong>Exam</strong> <strong>Review</strong><br />
Multiple Choice<br />
Identify the choice that best completes the statement or answers the question.<br />
____ 1.<br />
Identify the congruent triangles in the figure.<br />
a. ∆KLJ ≅ ∆ONM c. ∆LJK ≅ ∆OMN<br />
b. ∆KJL ≅ ∆OMN d. ∆JKL ≅ ∆ONM<br />
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.<br />
____ 2. 3, 9, 10<br />
a. Yes; the third side is the longest.<br />
b. No; the sum of the lengths of two sides is not greater than the third.<br />
c. No; the first side is not long enough.<br />
d. Yes; the sum of the lengths of any two sides is greater than the third.<br />
Short Answer<br />
Find the measures of the sides of ∆ABC and classify the triangle by its sides.<br />
3. AÊ<br />
Ë<br />
Á 5, − 2 ˆ¯˜, B Ê<br />
Ë<br />
Á7, 2ˆ¯˜,<br />
C Ê<br />
Ë<br />
Á 3, 5 ˆ¯˜<br />
Find each measure.<br />
4. m∠1, m∠2, m∠3<br />
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Name: ________________________<br />
ID: A<br />
Name the congruent angles and sides for the pair of congruent triangles.<br />
5. ∆SKL ≅ ∆CFG<br />
Refer to the figure. ∆ARM, ∆MAX, and ∆XFM are all isosceles triangles.<br />
6. What is m∠RAM ?<br />
7. If m∠FXA = 96, what is m∠FXM ?<br />
8. Triangle FJH is an equilateral triangle. Find x and y.<br />
9. Triangle RSU is an equilateral triangle. RT bisects US. Find x and y.<br />
2
Name: ________________________<br />
ID: A<br />
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,<br />
JF = 7 and HI = 3z − 4, find x, y, and z.<br />
11. ZC is an altitude, ∠CYW = 9x + 38, and ∠WZC = 17x. Find m∠WZC.<br />
Determine the relationship between the lengths of the given sides.<br />
12. ZX , YX<br />
13. Find the measure of each interior angle for a regular pentagon. Round to the nearest tenth if necessary.<br />
14. Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary.<br />
3
Name: ________________________<br />
ID: A<br />
Complete the statement about parallelogram ABCD.<br />
15. ∠CDA ≅<br />
Determine whether the quadrilateral is a parallelogram. Justify your answer.<br />
16.<br />
Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.<br />
17. A(1, − 6), B(−1, − 3), C(−2, 7), D(0, 4); Slope Formula<br />
Quadrilateral ABCD is a rectangle.<br />
18. If AG = −4k + 24 and DG = 9k + 102, find BD.<br />
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Name: ________________________<br />
ID: A<br />
19. In rhombus YZAB, if YZ =12, find AB.<br />
Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square.<br />
List all that apply.<br />
20. A(5, 10), B(4, 10), C(4, 9), D(5, 9)<br />
21. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.<br />
22. For trapezoid JKLM, A and B are midpoints of the legs. Find AB.<br />
23. Find the geometric mean between each pair of numbers.<br />
28 and 7<br />
5
Name: ________________________<br />
ID: A<br />
24. Find the measure of the BD.<br />
25. Find x.<br />
26. Find x and y.<br />
27. Find x and y.<br />
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Name: ________________________<br />
ID: A<br />
28. Find the measure of the angle to the nearest tenth of a degree.<br />
cos Y = 0.5135<br />
29. Dante is standing at horizontal ground level with the base of the Empire State Building in New York City.<br />
The angle formed by the ground and the line segment from his position to the top of the building is 48.4°.<br />
The height of the Empire State Building is 1472 feet. Find his distance from the Empire State Building to the<br />
nearest foot.<br />
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<br />
ground miles. About how far above sea level is the rocket ship after its climb?<br />
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<br />
of elevation from the hiker to the deer is 15°, find the distance from the hiker to the deer.<br />
Find each measure using the given measures of ∆KLM . Round measures to the nearest tenth.<br />
32. If m∠L = 48.4, m∠K = 24.5, and l = 37.9, find k.<br />
The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest<br />
hundredth if necessary.<br />
33. r = 13.1 km, d = ? , C = ?<br />
34. Find the exact circumference of the circle.<br />
7
Name: ________________________<br />
ID: A<br />
Use the diagram to find the measure of the given angle.<br />
35. m∠BAC<br />
36. m∠CAE<br />
37. In ñO, EC and AB are diameters, and ∠BOD ≅ ∠DOE ≅ ∠EOF ≅ ∠FOA.<br />
Find m arc BC.<br />
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Name: ________________________<br />
ID: A<br />
38. In ñU , TS = 15, UQ = US. Find mPR.<br />
39. Find x. Assume that segments that appear tangent are tangent.<br />
Find the measure of the numbered angle.<br />
40.<br />
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Name: ________________________<br />
ID: A<br />
Find x. Assume that any segment that appears to be tangent is tangent.<br />
41.<br />
42. Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.<br />
43. Find the area of the figure. Round to the nearest tenth if necessary.<br />
44. Find the area of the figure. Round to the nearest tenth if necessary.<br />
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Name: ________________________<br />
ID: A<br />
45. Find the area of the figure. Round to the nearest tenth if necessary.<br />
46. Find the area of a circle having a circumference of 34π. Round to the nearest tenth. Use 3.14 for pi.<br />
Find the area of the figure. Round to the nearest tenth if necessary.<br />
47.<br />
48.<br />
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Name: ________________________<br />
ID: A<br />
Find the lateral area of each prism. Round to the nearest tenth if necessary.<br />
49. The dimension labeled 10 is the height of the prism.<br />
50.<br />
51.<br />
Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as<br />
well as in your final answer.<br />
52.<br />
12
Name: ________________________<br />
ID: A<br />
Find the surface area of the cylinder. Use 3.14 for pi and round your answer to the nearest tenth.<br />
53.<br />
Find the surface area of the regular pyramid. Round to the nearest tenth if necessary.<br />
54.<br />
Find the volume of the prism. Round to the nearest tenth if necessary.<br />
55.<br />
13
Name: ________________________<br />
ID: A<br />
Find the volume of the cone. Use 3.14 for π. Round to the nearest tenth.<br />
56.<br />
57. Baseballs and softballs come in different sizes for different types of leagues. If the diameter of a baseball is 3<br />
inches and a softball has a diameter of 3.8 inches, find the difference between the volumes of the two balls.<br />
Use 3.14 for π. Round to the nearest tenth.<br />
Write a two-column proof.<br />
58. Given: R is the midpoint of SU ; SV ≅ UV .<br />
Prove: ∆RSV ≅ ∆RUV<br />
59. If FG ⊥ IJ and IG ≅ JG, then FI ≅ FJ .<br />
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Name: ________________________<br />
ID: A<br />
60. A triangle is formed by three kitchen appliances as shown in the figure. The distances shown are measured in<br />
feet. What is wrong with the labels on the triangle?<br />
Essay<br />
61. The vertices of a triangle are LÊ<br />
Ë<br />
Á 1,3 ˆ¯˜, M Ê<br />
Ë<br />
Á4,0ˆ¯˜,<br />
N Ê<br />
Ë<br />
Á −4,1 ˆ¯˜ .<br />
a. Graph the triangle.<br />
b. Use the Distance Formula to find the length of each side to the nearest tenth.<br />
c. LO is a median of the triangle. What are the coordinates of point O? Explain.<br />
d. Graph median LO.<br />
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