Download a || b

Geometry/Trig
Quiz 3-1, 3-2, 3-3
Name __________________________
Date ______________ Block _______
I. Identify the types of angles.
(Lines aren’t necessarily parallel).
c
d
1 2
3 15
4 9
5 10
16 6
8 7
b
11 13
12 14
a
1) 3 and 8
_____________________________
2) 3 and 7
_____________________________
3) 1 and 15
_____________________________
4) 15 and 11
_____________________________
5) 8 and 13
_____________________________
6) 13 and 14
_____________________________
7) 15 and 9
_____________________________
8) 5 and 6
_____________________________
II. In the below diagrams, solve for the missing variables. Leave any non-integer answers as
simplified fractions.
10)
9)
xº
11)
2xº
130º
52º
yº
zº
70º
(3y+11)º
Hint: Set up
& solve a
system of
equations.
16º
68º
x = _____
y = _____
x = _____
x = _____
z = _____
y = _____
y = _____
III. Use the diagram to the right to name each figure that is described. You must use proper notation.
12) Name two parallel lines. _________________
13) Name two intersecting lines. _____________
14) Name two skew lines. __________________
G
15) Name two parallel planes. _____________________
F
E
16) Classify GF and AB as parallel, intersecting or skew.
____________
17) Classify GE and DB as parallel, intersecting or skew.
____________
18) Classify DE and DF as parallel, intersecting or skew.
____________
D
H
A
C
B
IV. Complete the below proofs.
19)
t
Given:
k || l
Prove:
1 is supplementary to 7
1
4
3
2
5
6
8
7
k
l
Reasons
Statements
1. ________________________________
1. ______________________________
2.
2. ______________________________
1 and 4 are supplementary
______________________________
3. ________________________________
3.
4. ________________________________
4.
5. ________________________________
5. _____________________________
6.
6. _____________________________
1 is supplementary to 7
20) Given:
1 is supplementary to 7
Prove:
Vertical Angles are Congruent
Use the diagram above.
k || l
Statements
1.
Definition of Supplementary Angles
Reasons
1 and 7 are supplementary
1. ______________________________
2. ________________________________
2. ______________________________
3. ________________________________
3.
4.
4. ______________________________
m1 + m7 = m7 + m8
Definition of Linear Pair
5. ________________________________
5.
Subtraction
6. ________________________________
6. ______________________________
______________________________
21) Note: this proof can be completed many different ways (minimum of 4 steps!!)
Given:
k || l
Statements
Prove:
3  6
Use the diagram above.
Reasons
Geometry/Trig
Quiz 3-1, 3-2, 3-3
Page 3
l
m
22)
Given:
j || k; 1  5
Prove:
l || m
2
6
3
5
1
4
Statements
j
k
Reasons
1. ________________________________
1. ______________________________
2.
2. ______________________________
1  2
______________________________
3. ________________________________
3.
Given
4.
2  5
5. ________________________________
4. _____________________________
5. ______________________________
______________________________
a
23)
1
Given:
a || b ; c || d
Prove:
13 is supplementary to 8
5
9
13
Statements
2
6
10
14
b
3
7
11
15
12
16
4
8
c
d
Reasons
1. ________________________________
1. ______________________________
2.
2. ______________________________
13  15
______________________________
3.
c || d
3.
Given
4. ________________________________
4. If lines are parallel, then corresponding
angles are congruent.
5.
13  7; m13 = m7
6.
m7 + m8 = 180
7. ________________________________
8. ________________________________
5.
Substitution
6. ______________________________
7. ______________________________
8. ______________________________