Review: Semester Exam: Fall 2010 Pre-AP Geometry On Q1-Q4, solve each equation or system of equations.

1.

( )

2. 3.

4.

5.

6. Draw and label collinear points F, G,

and H which lie in plane T. Now draw

⃡ which intersects plane T at point J.

7. What object would represent the intersection of each combination below?

a) Two Lines b) A Line and a Plane

c) Two Planes d) A Point and a Plane

e) Three Planes f) Two opposite rays

8. Point B is between A and C. Find AB if AC = 56, BC = x, and AB = x

2.

9. Find the midpoint of the segment with endpoints (-6, 3) and (2, -3).

10. The midpoint A of ̅̅ ̅̅ has coordinates (-9, 5, 1). Find the coordinates of S if point M is at (9, -3, 4).

11. Find the length of the segment with endpoints (-2, -5) and (3, 7).

12. M is the midpoint of ̅̅ ̅̅ . Find the value of x if AM = 3x + 20 and AB = 12x – 8.

13. Given mABC = 94, find mABD.

14. Let (4x – 2)° represent the measure of an acute angle. What are the possible values of x written as a compound inequality?

15. Is it possible to construct a triangle with side lengths of 5, 7, and 12?

16. Is it possible to construct a triangle with side lengths of 18, 30, and 47?

17. Is it possible to construct a triangle

with side lengths of 10, 15, and 26?

18. Let A and B be supplementary

angles and let mA = (9x – 12)

and mB = (24x + 60)°. Find the

measures of A and B.

19. Find the value of x.

20. Find the values of x and y that make the polygon below regular.

21. Find the value of x.

22. The figure below shows two squares. The area of square I is 36 in

2 and the

area of square II is 196 in2. Find a and

b.

23. Find the values of x and y.

24. Find the perimeter and area of the triangle.

25. What are the next two terms of the sequence? 1, C, 5, G, 9, K, _____, _____ Find the function for the nth term.

26. 3, 10, 17, 24, 31, …

27. 12, 9, 6, 3, 0, …

28. 0,

, 3,

,

,

, …

29.

, 0,

,

,

,

,

, …

30. Space alien Google-eyed Goreki spent a year observing life on our planet. When autumn came, Google-eyed Goreki notices that the leaves on the trees surrounding his spacecraft turned golden brown and fell from their branches. He observes other trees in the area, and he notices that their leaves also turned brown and fell to the ground. When he makes a conjecture based on his observations, what type of reasoning is space alien Google-eyed Goreki using?

31. Find the value of x.

32. Referring to the information in Q26, space alien Google-eyed Goreki conjectures “Porve simp torkdom feek”. Translate his conjecture into English.

33. What counterexample does space alien Google-eyed Goreki need to see to disprove his conjecture?

34. For the given statement, write the if-then form, the converse, the inverse, and the contrapositive. Then give the truth value of each statement. All triangles are polygons.

y + 9

11x + 2y 5x - y

a

b

II

I

2x+20( )°

68°

35. Write another conditional statement that is equivalent to:

If m1 = 30, then 1 is acute.

36. If a triangle is scalene, then no sides of the triangle are congruent. Two sides of ∆ABC are congruent. What conclusion can be made AND which law of deductive reasoning was used?

37. If an angle is an obtuse angle, then its measure is greater than 90° but less than 180°. The . What conclusion can be made AND which law of deductive reasoning was used?

38. If I go to my friend’s house, then I will use his portable matter transportation unit to instantaneously travel to a planet in the general vicinity of Betelgeuse. If school is canceled, then I will go to my friend’s house. If I end up on a planet in the vicinity of Betelgeuse, then my dematerialized body will rematerialize so that my left arm is attached to center of my forehead. Using the Law of Syllogism, what conclusion can be made?

39. Find the measures of each lettered

angle.

40. Find the values of x.

41. In the figure, which of the following statements must be true?

I. a + b = d + e II. b + f + d = 180

III. b + f = c + e

42. Find the value(s) of that make .

43. Find the value of so that .

44. Find the values of x and y.

45. Draw a diagram such that , , and is skew to .

46. Find the value of x.

47. Find the slope of the line through the points (-6, 7) and (5, 2).

dcb

a36°

19° 13x 3( )°4x2( )° f

e

dc

b

a

l

m

n

90 10x( )°x2+3x( )°

2x + y( )°

2x y( )°

40°

60°

48. Find the value of k so that the line through the points (-5, 6) and (k + 2, 3k + 5) is parallel to the line through the points (6, -1) and (14, 1).

49. Graph the equation .

50. ̅̅ ̅̅ has endpoints at C(-2, 4) and P(2, -4). Find the coordinates of two

points A and E such that CAP and

CEP are congruent right isosceles triangles.

51. Find the equation of the line through (−9, 1) that is

perpendicular to the line described by the equation

. Write your answer in slope-intercept form.

52. Find the equation of the line through the points (−5, −1) and (−8, 4). Write your answer in standard form.

53. Find the values of x and y.

54. Find the values of x, y, and z.

For Q54-56, write a two-column proof . 55. Given: and

Prove: ̅̅ ̅̅ ̅̅ ̅̅

56.

Given: 2 3

Prove: 1 and 3 are supplementary

y 40°

x

27°

z

yx

60°

92°

48°

4

21

3

D

B

E

A

C 3

2

1