Download Int. Geometry Unit 2 Quiz Review (Lessons 1

Int. Geometry
Unit 2 Quiz Review (Lessons 1-4)
1
Match the examples on the left with each property, definition, postulate, and theorem on
the left
PROPERTIES:
1. Addition Property of =
2. Subtraction Property of =
3. Multiplication Property of =
4. Division Property of =
5. Distribution Property of =
6. Substitution Property of =
7. Reflexive Property of =
8. Symmetric Property of =
9. Transitive Property of =
10. Reflexive Property of Congruence
11. Symmetric Property of Congruence
12. Transitive Property of Congruence
a. GH = GH
b. If AB ≅ CD , then CD ≅ AB
c. If AB = CD and BC = DE, then
AB + BC = CD + DE
d. If ∠1 ≅ ∠2 and ∠2 ≅ ∠3 , then ∠1 ≅ ∠3
e. If 2m∠1 = 60 , then m∠1 = 30
AB
f. If
= 20 , then AB = 40
2
g. 3x + 6 = 3( x + 2)
h. If m∠1 = m∠2 , then m∠2 = m∠1
i. If AB = CD and CD = ED, then
AB = ED
j. If AB + BC = BC + CD, then AB = CD
k. ∠1 ≅ ∠1
l. If m∠1 + m∠2 = 90 and m∠2 = m∠3 ,
then m∠1 + m∠3 = 90
DEFINITIONS:
13. Definition of Angle Bisector
14. Definition of Midpoint
15. Definition of Segment Bisector
16. Definition of Congruent Angles
17. Definition of Congruent Segments
18. Definition of Right Angles
19. Definition of Acute Angles
20. Definition of Obtuse Angles
21. Definition of Straight Angle
m. Angles are congruent if and only if their
measures are equal
n. ∠CDB is a right angle if and only if
m∠CDB = 90
o. An angle is acute if and only if its
measure, x, is 0 < x < 90
p. Segments are congruent if and only if
their lengths are equal.
q. AB bisects ∠CAT if and only if
∠CAB ≅ ∠BAT
r. CD bisects AB if and only if it passes
through the midpoint of AB
s. M is the midpoint AB if and only if
AM = MB and A-M-B
t. An angle is obtuse if and only if its
measure, x, is 90 < x < 180
u. m∠ABC = 180 if and only if it’s a
straight angle
Int. Geometry
Unit 2 Quiz Review (Lessons 1-4)
2
POSTULATES
22. Segment Addition Postulate
23. Angle Addition Postulate
v. If B is between A and C, then
AB + BC = AC
w. If T is in the interior of ∠CAB , then
m∠CAT = m∠TAB = m∠CAB
Directions 24-27: Name the definition, property, postulate, or theorem that justifies each
statement. Refer to the diagram:
24. CT = CT
25. If AS bisects ∠CAP , then m∠CAS = m∠SAP
P
S
26. If A is the midpoint of CT , then CA = AT
C
A
T
27. m∠CAS + m∠SAP = m∠CAP
Directions 28: In the following two algebraic proofs, justify each statement with a
property from algebra.
Statement
2 x + 3 = 11
Reason
Given
a. 2 x = 8
a.______________
b. x = 4
b.______________
29.
Complete the following proof.
Given: ∠1 ≅ ∠3
Prove: ∠AEC ≅ ∠BED
B
A
C
1
2
3
E
D
Int. Geometry
30.
Unit 2 Quiz Review (Lessons 1-4)
3
Write an indirect proof.
B
Given: m∠1 ≠ m∠2
A
Prove: EB does not bisect ∠AEC
C
1
2
E
31.
A
Write a proof.
B
E
Given: AE = DE; CE = BE
Prove: AC = BD
32.
D
C
Write an indirect proof.
Given: 3 y + 12 ≠ 15
Prove: y ≠ 1
33.
Given: EG = FH
Prove: EF = GH
E
F
G
H
Int. Geometry
34.
Unit 2 Quiz Review (Lessons 1-4)
4
Given: 𝑚∠1 ≠ 𝑚∠3
B
Prove: 𝑚∠𝐴𝐸𝐶 ≠ 𝑚∠𝐷𝐸𝐵
A
C
1
2
3
E
Selected Answers:
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
28.
c
f
g
a
i
b
q
r
p
o
u
w
Def. of an angle bisector
Angle Addition Postulate
a. Subtraction b. Division
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
22.
24.
26.
j
e
l
h
k
d
s
m
n
t
v
Reflexive Property
Midpoint Definition
Note with the proofs, there are multiple solutions to these problems
29.
Statement
1. m∠2 = m∠2
2. m∠1 = m∠3
3. m∠1 + m∠2 = m∠3 + m∠2
4. m∠1 + m∠2 = m∠AEC
m∠2 + m∠3 = m∠BED
5. m∠AEC = m∠BED
Reason
1. Reflexive PoE
2. Given
3. Addition PoE
4. Angle Addition
Postulate
5. Substitution PoE
Relies on/uses to reach
Diagram
1 and 2
Diagram
3 and 4
D
Int. Geometry
30.
Unit 2 Quiz Review (Lessons 1-4)
5
Temporarily assume EB bisects ∠AEC
By the definition of an angle bisector ∠1 ≅ ∠2 .
This contradictions the given information m∠1 ≠ m∠2 , therefore our assumption
must be false and EB does not bisect ∠AEC
31.
Statement
1. AE = DE; CE = BE
2. AE + CE = DE + BE
3. AE + CE = AC
DE + BE = DB
4. AC = BD
32.
Reason
1. Given
2. Addition PoE
3. Segment Addition
Postulate
4. Substitution PoE
Relies on/uses to reach
1
Diagram
2 and 3
Temporarily assume y = 1.
Then 3 y + 12 = 3 (1) + 12 = 15
This contradicts our given information, 3 y + 12 ≠ 15 . Therefore our assumption
must be false and y ≠ 1
33.
Statement
1. EF+FG=EG and
FG+GH=FH
2. EG = FH
3. EF+FG = FG+GH
4. FG = FG
5. EF = GH
34.
Reason
1. Segment Addition
Postulate
2. Given
3. Substitution PoE
4. Reflexive PoE
5. Subtraction PoE
Relies on/uses to reach
Diagram
2 and 3
Diagram
3 and 4
Temp. assume that 𝑚∠𝐴𝐸𝐶 = 𝑚∠𝐷𝐸𝐵. The Angle Addition Postulate allows us
to say 𝑚∠𝐴𝐸𝐶 = 𝑚∠1 + 𝑚∠2 and 𝑚∠𝐷𝐸𝐵 = 𝑚∠2 + 𝑚∠3. Since
we assumed 𝑚∠𝐴𝐸𝐶 = 𝑚∠𝐷𝐸𝐵 by the Substitution PoE we
get 𝑚∠1 + 𝑚∠2 = 𝑚∠2 + 𝑚∠3 . The 𝑚∠2 = 𝑚∠2 by the Reflexive
PoE which means by the Subtraction PoE we have 𝑚∠1 = 𝑚∠3, but this
contradicts the given information that : 𝑚∠1 ≠ 𝑚∠3 which means our
assumption is false and 𝑚∠𝐴𝐸𝐶 ≠ 𝑚∠𝐷𝐸𝐵.