Geometry Fall Semester Review



Geometry Fall 2013 Semester Review

Chapter 1

Use the figure for #1-4. Name each of the following.

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1. two opposite rays

2. a point on BC

3. the intersection of plane N and plane T

4. a plane containing E, D, and B

5. Draw ray with end point P that passes through Q

6. Two planes intersect at a ________.

7. Two lines intersect at a _______.

8. A line and a plane intersect at a _________.

9. M is between N and O, MO = 15 and MN = 7.6. Find NO.

10. S is the midpoint of TV, TS = 4x -7 and SV = 5x - 15. Find TS, SV, and TV.

11. LH bisects GK at M. GM = 2x +6 and GK = 24. Find x.

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12. K is in the interior of (LMN, m(LMK = 52( and m(KMN = 12(. Find m(LMN.

13. BD bisects (ABC, m(ABD = (1/2y + 10)( and m(DBC = (y + 4)(. Find m(ABC.

14. m(WYZ = (2x - 5)( and m(XYW = (3x + 10)(. Find the value of x.

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15. _______________ angles are two angles in the same plane with a common vertex and a common side, but no common interior points. After filling in the blank, draw an example.

16. A ____________ ________ of angles is a pair of adjacent angles whose noncommon sides are opposite rays. After filling in the blank, draw an example.

17. Complementary angles are two angles whose measures have a sum of __________.

18. Supplementary angles are two angles whose measures have a sum of __________.

19. m(A = 64.1( and m(B = (4x – 30)(.

a. What is the supplement of (A?

b. What is the compliment of (B?

20. m(XYZ = 2x( and m(PQR = (8x – 20)(. If (XYZ and (PQR are supplementary, find the measure of each angle.

21. What is the circumference and area of a circle with a radius of 2 cm?

22. What is the circumference and area of a circle with a diameter of 12 ft?

23. Find the area and perimeter of each figure.

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24. Find the coordinates of the midpoint of MN with endpoints M (-2, 6) and N (8, 0).

25. K is the midpoint of HL. H has coordinates of (1, -7) and K has coordinates (9, 3). Find the coordinates of L.

26. Find the distance, to the nearest tenth, between S (6, 5) and T (-3, -4).

27. Find the lengths of AB and CD and determine whether they are congruent.

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28. A figure has vertices at X (-1, 1), Y (1, 4) and Z (2, 2). After a transformation, the image of the figure has vertices at X’ (-3, 2), Y’ (-1, 5) and Z’ (0, 3). Draw the preimage and the image. Identify the transformation.

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29. What transformation is suggested by the wings of an airplane?

30. Given points P (-2, -1) and Q (-1, 3), draw PQ and its reflection across the y-axis.

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31. Find the coordinates of the image of F (2, 7) after the translation

(x, y) ( (x + 5, y – 6).

Chapter 2

32. Find the next item in the pattern.

a. 0.7, 0.07, 0.007, …

b. [pic] [pic] [pic] …

33. Determine if each conjecture is true. If false, give a counterexample.

a. The quotient of two negative numbers is a positive number.

b. Every prime number is odd.

c. The square of an odd integer is even.

34. Identify the hypothesis and conclusion. If a triangle has one right angle, then it is a right triangle.

35. Write the converse, inverse, and contrapositive of the conditional statement “If Maria’s birthday is February 29, then she was born in a leap year.”

Chapter 3

36. Identify each of the following.

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a. One pair of parallel segments

b. One pair of skew segments

c. One pair of perpendicular segments

d. One pair of parallel planes

37. Identify each of the following.

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a. One pair of alternate interior angles

b. One pair of corresponding angles

c. One pair of alternate exterior angles

d. One pair of same-side interior angles

e. One pair of parallel lines

f. The transversal

38. What is the shortest segment? Write and solve an inequality for x.

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39. State how the angles are related then find the unknown angle measures.

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a. m(1 = 120(, m(2 = 60x(

b. m(2 = (75x – 30)(, m(3 = (30x + 60)(

c. m(3 = (50x + 20)(, m(4 = (100x – 80)(

d. m(3 = (45x + 30)(, m(5 = (25x + 10)(

40. Solve to find x and y in the diagram.

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41. Use the slope formula to determine the slope of the line that passes through M (3, 7) and N (-3, 1).

42. Graph each pair of lines. Use slopes to determine whether they are parallel, perpendicular, or neither. AB and XY for A (-2, 5), B (-3, 1), X (0, -2), and Y (1, 2).

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43. What is the slope of the line y = 3x +2?

44. Write an equation of a line that is parallel to y = 3x + 2.

45. Write an equation of a line that is perpendicular to y = 3x + 2.

46. Write an equation of a line that coincides with y = 3x + 2.

47. Write the equation of a line in slope-intercept form that passes through (-1, 3) and (3, -5). Then, graph the line.

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48. Write the equation of a line in y=mx + b form that passes through (5, -1) with slope 2/5. Then, graph the line.

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49. Solve each equation for y. Are the lines parallel, intersecting or coinciding?

a. 2y = 4x + 12

b. 4x – 2y = 8

Chapter 4A

50. Classify each triangle by its angles AND side lengths.

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a. (MNQ

b. (NQP

c. (MNP

51. Find the side lengths of the triangle.

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52. The measure of one of the acute angles in a right triangle is 23(. What is the measure of the other acute angle?

53. Find m(ABD

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54. Find m(N and m(P

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55. (ABC ( (JKL

a. AB = 2x + 12 and JK = 4x – 50. Find x and AB.

b. AC ( _____

c. (C ( _____

d. (K ( _____

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