Download Geometry/Trig Name: Unit 3 Review Packet – Answer Key Date

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
page
8
page
9
page
10
Document related concepts
no text concepts found
Transcript 
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Answer Key
Date: ___________________________
Section I – Name the five ways to prove that parallel lines exist.
1. If corresponding angles are congruent, then lines are parallel.
2. If alternate interior angles are congruent, then lines are parallel.
3. If alternate exterior angles are congruent, then lines are parallel.
4. If same side interior angles are supplementary, then lines are parallel.
5. If same side exterior angles are supplementary, then lines are parallel.
Section II – Identify the pairs of angles. If the angles have no relationship, write none.
1. 7 & 11
None
2. 3 & 6
Alternate Interior Angles
3. 8 & 16
Corresponding Angles
4. 2 & 7
Alternate Exterior Angles
5. 3 & 5
Same Side Interior Angles
6. 1 & 6
None
7. 1 & 6
None
8. 1 & 4
Vertical Angles
1 2
3 4
a
b
5 6
7 8
Section III – Fill In
Vertical angles are congruent.
If lines are parallel, then corresponding angles are congruent.
If lines are parallel, then alternate interior angles are congruent.
If lines are parallel, then alternate exterior angles are congruent.
If lines are parallel, then same side interior angles are supplementary.
If lines are parallel, then same side exterior angles are supplementary.
9 10
11 12
13 14
15 16
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 2 – Answer Key
Date: ___________________________
Section IV – Determine which lines, if any, are parallel based on the given information.
1.) m1 = m9
c // d
2.) m1 = m4
None
3.) m12 + m14 = 180
a // b
4.) m1 = m13
None
5.) m7 = m14
c // d
6.) m13 = m11
None
7.) m15 + m16 = 180
None
8.) m4 = m5
a //b
1 2
3 4
a
b
5 6
7 8
c
9 10
11 12
13 14
15 16
d
Section IV – Determine which lines, if any, are parallel based on the given information.
1. m1 = m4
a // b
2. m6 = m8
t // s
3. 1 and 11 are supplementary
4. a ^ t and b ^ t
5. m14 = m5
None
a // b
a
None
b
6. 6 and 7 are supplementary t // s
7. m14 = m15
8. 7 and 8 are supplementary
9. m5 = m10
10. m1 = m13
k // m
None
m
15
13
k // m
k
12
11
9
8
10
None
1
2
3
4
14
5
6
t
7
s
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 3 – Answer Key
Date: ___________________________
J
Section V - Proofs
1. Given: GK bisects JGI; m3 = m2
G
Prove: GK // HI
Statements
1. GK bisects JGI
1
2
K
Reasons
1. Given
3
I
2. m1 = m2
2. Definition of an Angles Bisector
3. m3 = m2
3. Given
4. m1 = m3
4. Substitution
5. GK // HI
5. If corresponding angles are congruent, then the lines are
parallel.
2. Given: AJ // CK; m1 = m5
H
A
Prove: BD // FE
C
Reasons
Statements
1. AJ // CK
1. Given
2. m1 = m3
2. If lines are parallel, then
corresponding angles are
congruent.
3. m1 = m5
3. Given
4. m3 = m5
4. Substitution
5. BD // FE
5. If corresponding angles are
congruent, then the lines are
parallel.
1
B
F
2
4
5
J
K
3
D
E
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 4 – Answer Key
Date: ___________________________
3. Given: a // b; 3 @ 4
Statements
1. a // b
Prove: 10 @ 1
1
a
3
5
Reasons
6
1. Given
2. 4 @ 7
2. If lines are parallel then
alternate interior angles
are congruent.
3. 3 @ 4
3. Given
4. 3 @ 7
4. Substitution
5. 1 @ 3; 7 @ 10
5. Vertical Angles Theorem
6. 10 @ 1
6. Substitution
4. Given: 1 and 7 are supplementary.
Prove: m8 = m4
8
7
b
9
10
d
c
1
b
a
Statements
2
4
Reasons
4
6
8
3
5
7
2
1. 1 and 7 are supplementary
1. Given
2. m1 + m7 = 180
2. Definition of Supplementary Angles
3. m6 + m7 = 180
3. Angle Addition Postulate
4. m1 + m7 = m6 + m7
4. Substitution
5. m1 = m6
5. Subtraction Property
6. a // b
6. If corresponding angles are congruent, then the
lines are parallel.
7. m8 = m4
7. If lines are parallel, then corresponding angles are
congruent.
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 5 – Answer Key
Date: ___________________________
5. Given: ST // QR; 1 @ 3
Prove: 2 @ 3
P
Reasons
Statements
1. ST // QR
1. Given
2. 1 @ 2
2. If lines are parallel, then
corresponding angles are
congruent.
1
S
3. 1 @ 3
3. Given
4. 2 @ 3
4. Substitution
Q
3
T
2
R
6. Given: BE bisects DBA; 1 @ 3 Prove: CD // BE
Reasons
Statements
1. BE bisects DBA
1. Given
2. 2 @ 3
2. Definition of an Angle Bisector
3. 1 @ 3
3. Given
4. 2 @ 1
4. Substitution
5. CD // BE
5. If alternate interior angles are congruent, then the lines are
parallel.
C
B
2 3
1
D
E
A
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – page 6 – Answer Key
Date: ___________________________
7.
Given: AB // CD; BC // DE
Reasons
Statements
Prove: 2 @ 6
1. AB // CD
1. Given
2. 2 @ 4
2. If lines are parallel, then alternate
interior angles are congruent.
3. BC // DE
3. Given
4. 4 @ 6
4. If lines are parallel, then alternate
interior angles are congruent.
5. 2 @ 6
5. Substitution
B
D
6
2
A
8.
1
3
5
7
C
E
Given: AB // CD; 2 @ 6
Reasons
Statements
4
Prove: BC // DE
1. AB // CD
1. Given
2. 2 @ 4
2. If lines are parallel, then alternate interior angles are congruent.
3. 2 @ 6
3. Given
4. 4 @ 6
4. Substitution
5. BC // DE
5. If alternate interior angles are congruent, then the lines are
parallel.
B
D
6
2
A
1
3
4
C
5
7
E
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – page 7– Answer Key
Date: ___________________________
Section VI – Solve each Algebra Connection Problem.
1.
2.
w
x
4x - 5
z + 57
23y
65
37 2y
w = 37
Equations:
37 = w
x + 37 = 180
2y + 37 = 180
z + 57 = 143
x = 143
y = 71.5
Equations:
65 + 23y = 180
65 = 4x – 5
125
x = 17.5
y=5
z = 86
Equations:
30 + 75 = 5x
30 + 75 + y = 180
3.
30
Equation:
6x + x + 12 = 8x + 1
4.
x + 12
75
y
5x
6x
8x + 1
x = 21
y = 75
x = 11
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – page 8
Date: ___________________________
Section VIII - Classify each triangle by its sides and by its angles.
1.
2.
A
D
3. G
60
B
59
F
C
Scalene
Acute
E
H
L
5.
O
M
20
I
Scalene
Obtuse
6.
42
55
100
Isosceles
Right
K
4.
J
45
Q
P
35
75
30
R
N
Scalene
Right
Scalene
Obtuse
7. In DABC which side is the longest? AB
8. In DDEF which side is the longest? DE
Isosceles
Acute
the shortest? AC
Which two have the same length? DF = FE
9. In DGHI which side is the longest? GI
the shortest? GH
10. In DJKL which side is the longest? JK
the shortest? JL
11. In DMNO which side is the longest? NO
the shortest? MO
12. In DPQR which side is the shortest? QR Which two have the same length? PQ = PR
In each triangle, name the smallest angle and the largest angle.
A
8
D
10
I
10
15
8
B
C
9
E
6
F
12
G
H
7
smallest
<C
smallest
<D
smallest
<I
largest
<B
largest
<E
largest
<H
36
108
108
144
108
108
144
Hexagon
720
360
9
19
80
Scalene
Acute
Nonagon
1260
140
360
40
27
6
Hexagon
9
360
60
4
Quadrilateral
360
90
360
90
Related documents