Download Proofs Review - Answer Key

Geometry/Trig 2
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
J
1. Given: GK bisects JGI; m3 = m2
G
Prove: GK || HI
1. GK bisects JGI
13 14
15 16
d
Section II - Proofs
Statements
9 10
11 12
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; 1  3
4. Substitution
5. GK || HI
5. If two lines are cut by a transversal and corresponding
angles are congruent, then the lines are parallel.
H
Geometry/Trig 2
Unit 3 Proofs Review – Answer Key
2. Given: AJ || CK; m1 = m5
Page 2
A
Prove: BD || FE
C
Reasons
Statements
1. AJ || CK
1. Given
2. m1 = m3
1  3
2. If two parallel lines are
cut by a transversal, then
corresponding angles are
congruent.
3. m1 = m5
3. Given
4. m3 = m5
3  5
4. Substitution
5. BD || FE
5. If two lines are cut by a
transversal and
corresponding angles are
congruent, then the lines are
parallel.
3. Given: ST || QR; 1  3
1
B
F
2
3
4
5
J
E
K
Prove: 2  3
D
P
Reasons
Statements
1. ST || QR
1. Given
2. 1  2
2. If two parallel lines are cut by
a transversal, then corresponding
angles are congruent.
3. 1  3
3. Given
4. 2  3
4. Substitution
S
Q
2
1
3
T
R
4. Given: a || b; 3  4
Statements
Prove: 10  1
Reasons
1
a
1. Given
2. 1  3
2. Vertical Angles Theorem
3. 1  4
3. Substitution
4. a || b
4. Given
5. 4  7
5. If lines are parallel,
then alternate interior
angles are congruent.
6. 1  7
6. Substitution
7. 7  10
7. Vertical Angles Theorem
8. 1  10
8. Substitution
6
Prove: 1 and 7 are supplementary.
9
10
d
Reasons
1
b
a
a || b
8
7
b
c
5. Given: a || b
1.
2
4
5
1. 3  4
Statements
3
4
6
8
3
5
7
2
1. Given
2. m1 + m4 = 180
2. Definition of Linear Pair/Angle Addition Postulate
3. m4 = m7; 4  7
3. If lines are parallel, then alternate interior angles
are congruent.
4. m1 + m7 = 180
4. Substitution
5. 1 and 7 are supplementary
5. Definition of supplementary angles
Geometry/Trig 2
Name: __________________________
Unit 3 Review Packet – Page 5 – Answer Key
Date: ___________________________
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 two lines are cut by a transversal and alternate interior angles
are congruent, then the lines are parallel.
C
B
2 3
1
D
E
A
Geometry/Trig 2
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 two parallel lines are cut by a transversal, then alternate
interior angles are congruent.
3. BC // DE
3. Given
4. 4  6
4. If two parallel lines are cut by a transversal, 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 two parallel lines are cut by a transversal, then alternate
interior angles are congruent.
3. 2  6
5. Given
4. 4  6
4. Substitution
5. BC // DE
3. If two lines are cut by a transversal and alternate interior angles
are congruent, then the lines are parallel.
B
D
6
2
A
1
3
4
C
5
7
E
Geometry/Trig 2
Name: __________________________
Unit 3 Review Packet – page 7– Answer Key
Date: ___________________________
Section VI – Solve each Algebra Connection Problem.
1.
2.
w
4x - 5
z + 57
x
23y
65
37 2y
125
w = 37
x = 143
x = 30
y = 71.5
y=5
z = 86
3.
4.
30
x + 12
y
75
6x
5x
8x + 1
x = 21
y = 75
5.
x = 11
6.
4x + 13
B
5x
6x
6x
4x + 25
A
4x + 25
D
4x + 17
83
80
C
x = 20
4x + 13
Is AB // DC? yes
x = 23
Is AD // BC? no
Geometry/Trig 2
Name: __________________________
Unit 3 Review Packet – page 8 – Answer Key
Date: ___________________________
Measure of
each interior
angle if it
was a regular
polygon
Sum of
the
Exterior
Angles
Measure of each
exterior angle if it
was a regular
polygon.
Number of
Diagonals that
can be drawn.
Number
of Sides
Name of
polygon
Sum of
interior
angles.
3
Triangle
180
60
360
120
0
4
Quadrilateral
360
90
360
90
2
5
Pentagon
540
108
360
72
5
6
Hexagon
720
120
360
60
9
7
Heptagon OR
Septagon
900
128.57
360
51.43
14
8
Octagon
1080
135
360
45
20
9
Nonagon
1260
140
360
40
27
10
Decagon
1440
144
360
36
35
n
n-gon
(n  2)180
(n  2)180
n
360
360
n
n(n  3)
2