Download ExamView - Sample Final Exam Questions - Geometry

Name: ______________________ Class: _________________ Date: _________
Sample Final Exam Questions - Semester 1 Final_Chapter 2
____
1. Find the value of x.
a.
b.
____
c.
d.
x=9
x=6
c.
d.
x = 5, y = 16
x = 5, y = 13
2. Find the values of x and y.
a.
b.
____
x = 36
x = 21
x = 6 , y = 13
x = 6 , y = 16
3. In the diagram, m∠1 = (2x + 4)° and m∠5 = (4x + 20)°. Which angle measures are possible?
a.
b.
178°
2°
c.
d.
1
26°
64°
ID: A
Name: ______________________
ID: A
In the diagram, AB = CD, BC = 3, AC = −7x − 14, and BD = −5x + 6. Match the numbered equation or
reason below with its corresponding letter (a - g) to show that AB = 53.
Equation
1. AB = CD, AC = −7x − 14,
BD = −5x + 6 , BC = 3
2.
3. AB + BC = AC
4. CD + BC = BD
5. AC = BD
6.
7. −2x − 14 = 6
8. −2x = 20
9. x = −10
10.
11. AB + 3 = 56
12. AB = 53
a.
b.
c.
d.
Reason
1. Given
2. Addition Property of Equality
3.
4. Segment Addition Postulate
5.
6. Substitution Property of Equality
7. Addition Property of Equality
8. Addition Property of Equality
9.
10. Substitution Property of Equality
11. Simplify
12. Subtraction Property of Equality
−7x − 14 = −5x + 6
Division Property of Equality
Addition Property of Equality
Segment Addition Postulate
____
4. Reason 3
____
5. Reason 5
e. AB + BC = CD + BC
f. Substitution Property of Equality
g. AB + 3 = −7(−10) − 14
6. Determine whether the conclusion is valid. If so, state the law of logic illustrated. If not, find a
counterexample.
If you live in Detroit, then you live in Michigan.
Statement
If you live in Michigan, then it is cold in December.
Statement
If you live in Detroit, then it is cold in December.
Conclusion
2
Name: ______________________
ID: A
7. Solve −3x − 10 = −6x + 11. Justify each step.
8. Solve −7 + 2(−4x − 3) = 11. Justify each step.
9. You are fencing in a rectangular pen to hold pigs. The formula for the perimeter P of the pen is P = 2l + 2w ,
where l is the length and w is the width. Solve the formula for w. Justify each step. Then find the width (in
feet) of the pen with a length of 190 feet and a perimeter of 490 feet.
Write the negation of the statement.
____ 10. The grapes are purple.
a. The grapes are green.
b.
The grapes are not purple.
____ 11. Let p be “you are a senior” and let q be “you are in high school.” Write the converse. Then decide whether it
is true or false.
a. If you are a senior, then you are in high school; true
b. If you are in high school, then you are a senior; false
c. If you are not a senior, then you are not in high school; false
d. If you are not in high school, then you are not a senior; true
____ 12. Let p be “you are a senior” and let q be “you are in high school.” Write the contrapositive. Then decide
whether it is true or false.
a. If you are a senior, then you are in high school; true
b. If you are in high school, then you are a senior; false
c. If you are not a senior, then you are not in high school; false
d. If you are not in high school, then you are not a senior; true
3
Name: ______________________
ID: A
____ 13. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the inverse. Then decide
whether it is true or false.
a. If an animal is a golden retriever, then it is a dog; true
b. If an animal is not a golden retriever, then it is not a dog; false
c. If an animal is a dog, then it is a golden retriever; false
d. If an animal is not a dog, then it is not a golden retriever; true
____ 14. Let p be “you are a pitcher” and let q be “you are on the baseball team.” Write the conditional statement
p → q in words. Then decide whether it is true or false.
a. If you are on the baseball team, then you are a pitcher; true
b. If you are a pitcher, then you are on the baseball team; false
c. If you are on the baseball team, then you are a pitcher; false
d. If you are a pitcher, then you are on the baseball team; true
____ 15. Let p be “a figure is a triangle” and let q be “a figure is a polygon.” Write the inverse ∼ p → ∼ q in words.
Then decide whether it is true or false.
a. If a figure is not a polygon, then it is not a triangle; true
b. If a figure is not a polygon, then it is not a triangle; false
c. If a figure is not a triangle, then it is not a polygon; false
d. If a figure is not a triangle, then it is not a polygon; true
Use the Law of Detachment to determine what you can conclude from the given information, if
possible.
____ 16. If you get an A on the test, then you will get a sticker. You get an A on the test.
a. You will get a sticker.
b. not possible
Name the property that the statement illustrates.
____ 17. ∠EFG ≅ ∠EFG
a. Reflexive Property of Angle Congruence
b. Transitive Property of Angle Congruence
c. Symmetric Property of Angle Congruence
Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain
your reasoning.
____ 18. The sum of the measures of the interiors angles of a polygon is 180(n − 2)°, where n is the number of sides. A
triangle is a polygon with three sides. So, the sum of the measures of its interior angles is 180°.
a.
b.
inductive reasoning; A pattern is used.
inductive reasoning; Facts are used.
c.
d.
4
deductive reasoning; A pattern is used.
deductive reasoning; Facts are used.
Name: ______________________
ID: A
State the postulate illustrated by the diagram.
____ 19.
a.
b.
Two Point Postulate
Line Intersection Postulate
c.
d.
Three Point Postulate
Line-Point Postulate
Use (H) to represent the hypothesis and (C) to represent the conclusion. Then rewrite the conditional
statement in if-then form.
____ 20. You are in France if you are in Paris.
a.
b.
c.
d.
(H) You are in Paris, (C) you are in France;
If you are in Paris, then you are in France.
(H) You are in Paris, (C) you are in France;
If you are in France, then you are in Paris.
(H) you are in France, (C) You are in Paris;
If you are in Paris, then you are in France.
(H) you are in France, (C) You are in Paris;
If you are in France, then you are in Paris.
____ 21. All 16-year-old people can drive.
a.
b.
c.
d.
(H) drive, (C) All 16-year-old people;
If a person can drive, then he or she is 16 years old.
(H) drive, (C) All 16-year-old people;
If a person is 16 years old, then he or she can drive.
(H) All 16-year-old people, (C) drive;
If a person can drive, then he or she is 16 years old.
(H) All 16-year-old people, (C) drive;
If a person is 16 years old, then he or she can drive.
5
Name: ______________________
ID: A
Identify the numbered statement or reason in the two-column proof.
Given
Prove
∠ABC is a right angle.
x=8
STATEMENTS
1. ∠ABC is a right angle.
2. m∠ABC = 90°
3.
4. (6x + 5)° + (5x − 3)° = 90°
5. 11x + 2 = 90
6.
7. x = 8
REASONS
1. Given
2.
3. Angle Addition Postulate
4. Substitution Property of Equality
5. Simplify.
6. Subtraction Property of Equality
7.
____ 22. What is Statement 3?

→
a.
b.


→
BA ⊥ BC
m∠ABD + m∠CBD = 90°
____ 23. What is Reason 7?
a. Division Property of Equality
b. Simplify.
c.
d.
m∠ABD = m∠CBD
2(m∠ABD) = 90°
c.
d.
Addition Property of Equality
Symmetric Property of Equality
6
Name: ______________________
ID: A
Identify the numbered statement or reason in the two-column proof.
Given
Prove
EH = 28, EF = 2x − 1, FG = x + 5, GH = x
x=6
STATEMENTS
1. EH = 28, EF = 2x − 1, FG = x + 5,
GH = x
2. EH = EG + GH
EG = EF + FG
3.
4.
5.
6.
7.
8.
EH = EF + FG + GH
28 = (2x − 1) + (x + 5) + x
REASONS
1. Given
2.
3.
4. Substitution Property of Equality
5. Simplify.
6. Subtraction Property of Equality
7. Division Property of Equality
8. Symmetric Property of Equality
6=x
x=6
____ 24. What is Reason 3?
a. Addition Property of Equality
b. Simplify.
c.
d.
Transitive Property of Equality
Substitution Property of Equality
____ 25. What is Statement 5?
a. 28 = 3x + 4
b. 28 = 4x + 4
c.
d.
24 = 4x
24 = 4x + 6
Which statements, if any, about the diagram are true?
____ 26.
←

→
a.
b.
Point Q is the midpoint of PT .
∠PQS and ∠SQT are supplementary.
c.
d.
7
∠PQT is a straight angle.
none of these
Name: ______________________
ID: A
____ 27.

→
c.
m∠AEB = 90°
Point E is the midpoint of AC .
d.
none of these
a.
∠ABE and ∠EBC are vertical angles.
c.
Points A, B, and C are collinear.
b.
BE is an angle bisector.
d.
none of these
a.
b.
JM and MG are congruent segments.
∠FMG and ∠HMG are a linear pair.
c.
d.
a.
b.
∠2 and ∠3 are complementary.
Points A, B, and D are collinear.
c.
d.
a.
EB is an angle bisector.
b.
←
→
____ 28.


→
____ 29.


→

→
MJ and MH are opposite rays.
none of these
____ 30.

→
8


→
BA and BC are opposite rays.
none of these
Name: ______________________
ID: A
Determine which statements about the diagram you cannot conclude.
____ 31.
←
→
a.
b.
Line n and BD intersect at point D.
Line m is perpendicular to plane S.
c.
d.
Points A, B, and C are collinear.
Line m intersects plane S at point C.
____ 32.
←

→
←

→
←

→
a.
MN and ST intersect.
c.
Line ™ and ST are coplanar.
b.
Plane Q contains points J, M, and N.
d.
Line ™ intersects MN at point N.
a.
b.
c.
d.
Lines p and q intersect at point F.
Points E, B, and C are collinear.
Line q is perpendicular to line p.
∠CAB and ∠BAD are supplementary.
e.
AB ⊥ CD
____ 33.

→
←
→
9
←

→
Name: ______________________
ID: A
____ 34.
←
→
←

→
a.
CD and AB are coplanar.
b.
c.
d.
Plane T and plane S intersect at AB .
Plane S contains points L, B, and E.
∠ACD and ∠DCB are vertical angles.
e.
BE ⊥ plane S
←

→
←

→
35. Make and test a conjecture about the sum of any seven consecutive integers.
Copy and complete the two-column proof.
36. Given
Prove
AD = 63, BC = 41, AB = CD
CD = 11
STATEMENTS
1. AD = 63, BC = 41, AB = CD
2. AD = AC + CD
REASONS
1.
2. Segment Addition Postulate
3.
4. 63 = CD + 41 + CD
5. 63 = 2CD + 41
6.
7. 11 = CD
3. Substitution Property of Equality
4. Substitution Property of Equality
5.
6. Subtraction Property of Equality
7. Division Property of Equality
AC = AB + BC
10
Name: ______________________
ID: A
Copy and complete the flowchart proof.
←
→
←
→
37. Given
Prove
AC ⊥ BD
∠BEC ≅ ∠DEA
38. Given
Prove
B is the midpoint of AC .
2AB = AC
11
ID: A
Sample Final Exam Questions - Semester 1 Final_Chapter 2
Answer Section
1.
2.
3.
4.
5.
6.
7.
D
A
C, D
D
F
valid; Law of Syllogism
x = 7 ; Sample answer:
Equation
−3x − 10 = −6x + 11
3x − 10 = 11
3x = 21
x=7
8. x = −3 ; Sample answer:
Equation
−7 + 2(−4x − 3) = 11
−7 − 8x − 6 = 11
−8x − 13 = 11
−8x = 24
x = −3
Explanation and Reason
Write the equation; Given
Add 6x to each side,
Addition Property of Equality
Add 10 to each side;
Addition Property of Equality
Divide each side by 3;
Division Property of Equality
Explanation and Reason
Write the equation; Given
Multiply; Distributive Property
Combine like terms; Simplify.
Add 13 to each side;
Addition Property of Equality
Divide each side by –8;
Division Property of Equality
9.
Statement
P = 2l + 2w
2l + 2w = P
2w = P − 2l
P − 2l
w=
2
10.
11.
12.
13.
14.
15.
16.
17.
18.
Reason
Given
Symmetric Property of Equality
Subtraction Property of Equality
Division Property of Equality
The width is 55 feet.
B
B
D
D
D
C
A
A
D
1
ID: A
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
D
A
D
B
A
D
B
B, C
A, C
B
B
D
B, C
A, C, D
B, C
C, D, E
The sum of any seven consecutive integers is seven times the middle (fourth) number. Sample answer:
2 + 3 + 4 + 5 + 6 + 7 + 8 = 35 = 7(5) , 4 + 5 + 6 + 7 + 8 + 9 + 10 = 49 = 7(7) , −1 + 0 + 1 + 2 + 3 + 4 + 5 = 14 = 7(2)
36.
STATEMENTS
1. AD = 63, BC = 41, AB = CD
2. AD = AC + CD
AC = AB + BC
REASONS
1. Given
2. Segment Addition Postulate
3. AD = AB + BC + CD
3. Substitution Property of Equality
4. 63 = CD + 41 + CD
4. Substitution Property of Equality
5. 63 = 2CD + 41
5. Simplify.
6. 22 = 2CD
6. Subtraction Property of Equality
7. 11 = CD
7. Division Property of Equality
37. ∠BEC and ∠DEA are right angles, Right Angles Congruence Theorem
38. Definition of midpoint; AB = BC ; Segment Addition Postulate; AB + AB = AC ; Simplify.
2
Sample Final Exam Questions - Semester 1 Final_Chapter 2 [Answer Strip]
D
_______13.
D
_______
1.
D
_______14.
C
_______15.
A
_______
2.
A
_______16.
B
_______10.
C, D 3.
_______
A
_______17.
B
_______11.
D
_______
4.
F
_______
5.
D
_______12.
D
_______18.
ID: A
Sample Final Exam Questions - Semester 1 Final_Chapter 2 [Answer Strip]
A, C
_______27.
D
_______19.
B
_______28.
A
_______20.
D
_______24.
D
_______21.
B
_______29.
B
_______22.
B
_______25.
A
_______23.
B, C
_______26.
D
_______30.
ID: A
Sample Final Exam Questions - Semester 1 Final_Chapter 2 [Answer Strip]
C, D, E
_______34.
B, C
_______31.
A, C, D
_______32.
B, C
_______33.
ID: A