Download Geometry Pre-AP Name Fall Exam Review (PART 1) CHAPTER 1

Geometry Pre-AP
Fall Exam Review (PART 1)
CHAPTER 1: FOUNDATIONS OF GEOMETRY
1.1 – Understanding Points, Lines, and Planes
Use the figure to name each of the following:
1. Five points:
2. Two lines:
3. Two planes:
4. Point on BD :
Draw and label each of the following.
5. A segment with endpoints M and N
6. A ray with endpoint F that passes through G
Use the figure to name each of the following.
7. A line that contains A and C
8. A plane that contains A, D and C
Sketch a figure that shows each of the following.
9. Three coplanar lines that intersect in a common point
10. Two lines that do not intersect
1.2 – Measuring and Constructing Segments
Use the diagram for #11 and #12
11. GH = 4x -1 , and DH = 8. Find x.
12. GH bisects CF , CF = 2y -2 , and CD = 3y -11. Find CD.
Name
Suppose S is between R and T. Use the Segment Addition Postulate to solve for each variable.
13.
14.
1.3 – Measuring and Constructing Angles
15.
16.
Use the following diagram for #17 - #19. Classify the following angles.
17. BOA
18. EOD
Find the value of x
20. mAOC = 7x -2 , mDOC = 2x + 8, mEOD = 27
21. mAOB = 6x + 5, mBOC = 4x – 2, mAOC = 8x + 21
19. EOB
22. Q is in the interior of right PRS . If mPRQ is 4 times as large as mQRS , what is mPRQ ? Draw a Picture!
1.4 – Pairs of Angles
23. Name the pairs of vertical angles.
24.
25.
26.
27.
Determine whether each statement is true or false. If false, explain why.
28. If an angle is actue, then its complement must be greater than its supplement.
29. A pair of vertical angles may also form a linear pair.
30. If two angles are supplementary and congruent, the measure of each angle is 90.
31. If a ray divides an angle into two complementary angles, then the original angle is a right angle.
1.6 – Midpoint and Distance
32. Find the midpoint of MN with endpoints M(12, -7) and N(-5, -2)
33. M is the midpoint of QR . Q has coordinates ( -3, 5) and M has coordinates (7, -9). Find the coordinates of R.
Find the length of the given segments and determine if they are congruent.
34. DE and FG
35. DE and RS
The coordinates of the vertices of ABC are A(1, 4), B(-2, -1) and C(-3, -2).
36. Find the perimeter of ABC to the nearest tenth.
CHAPTER 2: GEOMETRIC REASONING
2.1 – Using Inductive Reasoning to Make Conjectures
37. About 5% of the students at Lubbock High School usually participate in the robotics competition. There are 526
students in the school this year. Make a conjecture about the number of students who will participate in the robotics
competition this year.
Show that each conjecture is false by finding a counterexample.
38. If 1 – y > 0, then 0 < y < 1.
39. For an real number x, x 3  x 2 .
Make a conjecture about each pattern. Write the next two items.
40. 2, 4, 16, …
41. -3, 6, -9, 12, …
Determine if each conjecture is true. If not, write or draw a counterexample.
42. In a triangle with one right angle, two if the sides are congruent.
43. If BD bisects ABC , then mABD  mCBD
44.
45. What is the difference between inductive and deductive reasoning?
2.2 – Conditional Statements
Identify the hypothesis and conclusion of each conditional. Underline the hypothesis once and the conclusion twice.
46. If an animal is a tabby, then it is a cat.
47. Four angles are formed if two lines intersect.
Write a conditional statement from the sentence.
48. You should monitor the heart rate of a patient who is ill.
Write the converse, inverse, and contrapositive of the conditional statement. Find the truth value of each.
49. If freezing rain is falling, then the air temperature is 32 o F of less.
Converse:
Inverse:
Contrapositive:
50. Write a conditional statement from the Venn diagram
Find a counterexample to show that the converse of each conditional is false.
51. If x = 5, then x 2  25
Converse:
Counterexample:
52. If two angles are vertical angles, then they are congruent.
Converse:
Counterexample:
2.5 – Algebraic Proof
Solve the following equations. Justify each step!
53. 5x – 3 = 4(x + 2)
54.
1
( p  16)  13
2
Identify the property that justifies each statement.
55. KL  PR , so PR  KL
56. 412 = 412
57. If a = b and b = 0, then a = 0
58. A  A
2.6 – Geometric Proof
59.
Fill in the blanks to complete the two-column proof
60.
Use the given plan to write a two-column proof.
61.
Use the given plan to write a two-column proof.
62.