Download Chapter 1 Review - Hartland High School

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Geometry Chapter 2 Test Review
Sections 2.1 – 2.7
Section 2.1: Use Inductive Reasoning
Use Inductive reasoning to find the next two numbers in each pattern.
1. 4, 16, 64, …
2. 2, 3, 5, 8, …
3. 1, 5, 9, 13, …
If the pattern indicated below is continued, what would be the total number of cubes in the 4 th stage of
the pattern? Make a conjecture.
4.
5.
6. Make a conjecture about the pattern of the given data. Find the sum of the 4th row.
2
2+4+2
2+4+6+4+2
Show the conjecture is false by finding a counterexample.
7. Any four-sided polygon is a square.
8. If a polygon has six sides, then it is a regular hexagon.
Section 2.2: Analyze Conditional Statements
For the given statement, write the CONVERSE, INVERSE, and the CONTRAPOSITIVE and indicate
whether each statement is true or false. Underline the hypothesis once, and the conclusion twice.
Then state the biconditional of this statement.
9. If two lines are perpendicular, then they intersect to form a right angle.
Converse:
Inverse:
Contrapositive:
Biconditional (Any valid definition can be written as a biconditional statement):
Geometry A Ch.2 Test Review
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Section 2.3: Apply Deductive Reasoning
Decide whether the following is valid or invalid: (Can you conclude the 3rd statement?)
10.
If you order the apple pie, then it will be served with ice cream.
Matthew ordered the apple pie.
Matthew was served ice cream.
11.
If you wear the school colors, then you have school spirit.
If you have school spirit, then the team feels great.
If you wear the school colors, then the team will feel great.
12.
If an obtuse angle is bisected, then two acute angles are obtained.
Angles A and  B are drawn.
Angles A and  B are obtuse angles.
13.
Jason lives further from school than Taylor.
Taylor lives further from school than Jack.
Jason lives further from school than Jack.
Section 2.4: Use Postulates and Diagrams
Use this diagram to answer the next questions as True or False.
D●
A
●
●
C
●
B
E●
F●
14. Points A, B, D, and C are coplanar.
15. EBA is a right angle.
16. Points E, B, and D are collinear.
17. FC  AB
CG EBC are vertical angles.
18. GABD and
19. AB contains C.
20. FC and DE intersect.
21. ABD and CBD are congruent angles.
22. mABD + mCBD = 180°.
23. ABD and CBD are adjacent angles.
24. ABD and CBD are supplementary angles.
25. ABD and CBD are a linear pair.
26. ABD  BCF.
27. mABE = 90°.
28. Intersecting lines always intersect at right angles.
29. Perpendicular lines always form right angles.
30. One plane always passes through three noncollinear
points.
Geometry A Ch.2 Test Review
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Section 2.4: Use Postulates and Diagrams (continued)
Match the postulate illustrated by the diagram.
A. Through any two points there exists there exists exactly one line.
B. Through any three noncollinear points there exists exactly one plane.
C. If two lines intersect, then their interaction is exactly one point.
D. If two points lie in a plane, then the line containing them lies in the plane.
E. If two planes intersect, then their intersection is a line.
F. A line contains at least two points.
G. A plane contains at least three noncollinear points.
31. If
then
32. If
then
33. If
then
34. If
then
Can the statement be assumed to be true from the diagram?
35. B, C, and D are collinear
36. AC  BE
37. CFE and AFE are a linear pair.
38. CFE  AFE
Section 2.5: Reason Using Properties from Algebra & Section 2.6: Using congruence Theorems
Name the property that justifies the conclusion or statement.
39. Given:
8x – 34 = 6
Conclusion: 8x = 40
40.
Given:
Conclusion:
–2x = 14
x = –7
41. Given:
x – 12 = 42
Conclusion: x = 54
42.
Given:
Conclusion:
4(m + 1)
4m + 4
43. Ifl  2 and 2  4, then l  4.
44.
XY  XY
45. If CDE  RST, then RST  CDE.
46.
If RZ = 4 and RZ + ST = 9, then 4 + ST = 9.
47. A  A
48.
If AB = CD and CD = EF, then AB = EF.
Geometry A Ch.2 Test Review
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Section 2.6: Prove Statements about Segments and Angles
49. Consider the following given information and the diagram. Find mABC.
GIVEN: ABC  CBD, mCBD = 50°, mCBE = 100°
Match a reason for each step of the proof.
50.
GIVEN: 2  3
PROVE: l  4
A. Transitive Property of Congruence
B. Given
C. Vertical Angles Congruence Theorem
51.
Statements
Reasons
1. 2  3
1.
2. 3  4
2.
3. 2  4
3.
4. l  2
4.
5. l  4
5.
GIVEN: m1 = m3
PROVE: mBED = mAEC
A.
B.
C.
D.
A●
Addition Property of Equality
Angle Addition Postulate
Given
Substitution Property of Equality
Statements
1.
B● C●
D●
2
1
3
E●
Reasons
m 3 = m1
1.
2. m3 + m2 = m1 + m2
2.
3. m3 + m2 = mBED
3.
4. m1 + m2 = mAEC
4.
5. mBED = mAEC
5.
Geometry A Ch.2 Test Review
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Section 2.6: Prove Statements about Segments and Angles (continued)
Solve for x.
AB  CD.
52.
2x
●
A
53. In ABCD, AB  CD.
2x+6
●
B
A
4x-2
●
C
2x + 12
B
●
D
C
D
54. AFB  BFC and BFC  CFD.
If mDFE  15 °, then what is mAFB ?
B●
●
A
C●
●
F
4x - 16
D●
●
E
Section 2.7: Prove Angle Pair Relationships
55. True or False
Vertical angles are always congruent.
56. True or False
Right angles are always congruent.
57. True or False
Linear pair angles are always adjacent.
58. True or False
Supplementary angles are always adjacent.
59. True or False
Complementary angles are always adjacent.
60. l and 2 form a linear pair. If ml = 20°, what is the m2? Hint: Draw a picture.
61. 3 and 4 are supplementary angles. 4 and 1 are vertical angles. If m4 = 60°,
what is the ml? Hint: Draw a picture.
62. 2 and 4 are each supplementary to 3. If m4 = 160°, then what is the m2? Hint: Draw a
picture.
63. 1 and 2 are complementary angles. If m1 = 40°, then what is the m2? Hint: Draw a
picture.
Geometry A Ch.2 Test Review
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Section 2.7: Prove Angle Pair Relationships (continued)
Use the diagram to answer the following questions.
64. If ml = 47°, then m2 =
65. m2 = 67°, then m4 =
Find the value of x and the value of each angle.
66. mABC = (2x + 2)°
67.
mCBD = (8x + 3)°
A
●
and mABD = 75°
53.
C
●
●
D
B●
68.
69.
(8x + 15)°
(2x + 5)°
(8x – 15)°
(3x + 5)°
Extra
Consider the following information.
You want to know the number of minutes that you can use on your $20 phone card. The card
company charges you $0.50 for the first minute and $0.10 for each addition minute.
70. (a.) What is the formula to solve this problem? Use m for the number of minutes.
(b.) How many minutes after the first minute can you use the phone card?
Ch.2 Test Review 3/2011
Geometry A Ch.2 Test Review
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