Name:
Ms. D’Amato
Date:
Block:
Identify Pairs of Lines and Angles
1. Definition: Parallel lines are
lines that do not
and
.
2. Definition: Perpendicular lines are
lines that
.
3. Definition: Skew lines are lines that
(If 2 lines are skew lines, there is no plane that contains both lines.)
C
B
Parallel, perpendicular or skew?
A
D
G
H
.
F
⃡ and 𝐹𝐺
⃡ are
𝐴𝐷
.
⃡𝐷𝐻 and ⃡𝐶𝐷 are
.
⃡ are
⃡𝐹𝐸 and 𝐴𝐷
.
E
4. Definition: Parallel planes are planes that do not
.
Draw two parallel planes:
5. Parallel and Perpendicular Postulates.
A. Parallel Postulate: If a line and a point that is not on the line are given, then there is
_____________ _______ line that can be drawn through the point that is parallel to the
line.
B. Perpendicular Postulate: If a line and a point that is not on the line are given, then there is
_____________ _______ line that can be drawn through the point that is perpendicular to
the line.
6. Definition: A transversal is a
.
7. Be able to identify these types of pairs of angles:
a.
b.
c.
d.
e.
Corresponding s
Alternate interior s
Alternate exterior s
Consecutive interior s (sometimes called same-side interior s)
Consecutive exterior s
Example:
Use the diagram at the right to name all the pairs of:
a. Corresponding s:
Occupying corresponding positions
____________
____________
____________
____________
b. Alternate exterior s:
____________
c. Alternate interior s:
____________
1
3
Lying outside the two lines
on opposite sides of the transversal
____________
5
8
2
4
6
7
Lying between two lines
on opposite sides of the transversal
____________
d. Consecutive interior s: Lying between the two lines on
the same side of the transversal
____________
____________
e. Consecutive exterior s: Lying outside the two lines on the same side of the transversal
____________
____________
Use Parallel Lines and Transversals
8. Postulate:
If two parallel lines are intersected by a transversal, then the corresponding
angles are congruent.
t
See the diagram at right. If we know that l // m,
then we can conclude that:
,
2
1
3
,
l
4
5
,
6
m
8
7
.
Trick:
.
9. Theorem: If 2 lines are parallel, then alternate interior s are congruent.
Examples:
a. If a // b, then:
a
,
1
4
and
b
2
3
5
8
b. If a // b and m3 = 60, then m1 =
6
7
.
m2 = _______, m4 = _______, m5 = _______, m6 =_______.
Trick:
.
10. Theorem: If 2 lines are parallel, then consecutive interior s are
.
Examples:
a. If l // m, then 4 supp 
and 3 supp 
.
b. If l // m and m4 = 70, then m5 =
Trick:
.
.
1 2
4 3
5 6
8 7
l
m
11. Theorem: If 2 lines are parallel, then alternate exterior angles are congruent.
1
Examples:
a. If c // d, then 1 ≅ 
and 2 ≅ 
4
.
3
2
c
5 6
8 7
b. If c // d and m1 = 150, then m7 = ________.
d
12. Consecutive exterior angles: If two parallel lines are cut by a transversal, then the following pairs
of angles are supplementary. (not a theorem)
t
Examples:
a. If l // m, then 1 supp 
and 2 supp 
b. If l // m and m1 = 55, then m7 =
.
.
2
1
3
l
4
5
6
7
8
13. Theorem: If a transversal is  to 1 of 2 parallel lines, then the transversal is  to the other line
also.
Examples:
a. Draw m  a and a // b.
b. Is m  b?
c. If lines c and d are parallel and line t is drawn perpendicular to d, then what conclusion
can you make?
Draw a diagram.
**Do not forget about vertical angles (equal) and linear pairs (supplementary)**
m