1. Lesson 3-1: Parallel Lines & Transversals
TARGETS
Identify relationships between two lines or two planes.
Name angle pairs formed by parallel lines and transversals
Targets

2. Content Standards G-CO.1 Experiment with transformations in the plane.
Mathematical Practices
2 Reason abstractly and quantitatively.
6 Attend to precision.
Targets

3. Alternate interior angles Alternate exterior angles
Corresponding anlges
Parallel line
Skew lines
Parallel planes
Transversal
Interior angles
Exterior angles
Consecutive interior angles
Targets

4. Lines & Planes (modeling)
LESSON 3-1: Parallel Lines & Transversals
Lines & Planes
Model the following situations in the items on your desk
Two lines intersect in a point
A line intersects a plane at a point
Two planes intersect in a line
Lines & Planes (modeling)

5. Parallel and Skew Parallel lines -
LESSON 3-1: Parallel Lines & Transversals
Parallel and Skew
Parallel lines -
Coplanar lines that DO NOT intersect
Parallel planes -
Planes that DO NOT intersect
Plane A
Plane B
Skew lines -
Lines that DO NOT
intersect and are not
coplanar
Lines l and m are skew lines
Parallel & Skew

6. Model the following situations in the items on your desk
LESSON 3-1: Parallel Lines & Transversals
Lines & Planes
Model the following situations in the items on your desk
1) Two lines are parallel.
2) Two planes are parallel
3) Two lines are skew
4) Two lines are parallel. Both lines intersect a plane in
2 distinct points.
5) Two lines intersect a plane in two distinct points.
The two lines are skew.
Modeling situations

7. EX 1: ID Parallel & Skew Relationships
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 1
Identify Parallel and Skew Relationships
A. Name all segments parallel to BC.
AD, EH, FG
B. Name a segment skew to EH.
AB, CD, BG, or CF
C. Name a plane parallel to plane ABG.
plane CDE
EX 1: ID Parallel & Skew Relationships

8. EX 1: ID Parallel & Skew Relationships
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 1
Identify Parallel and Skew Relationships
A. Name a plane that is parallel to plane RST.
plane WXY
B. Name a segment that intersects YZ.
WZ, XY, TS, or SY
C. Name a segment that is parallel to RX.
QW, TZ, or SY
EX 1: ID Parallel & Skew Relationships

9. Transversal line d A line that intersects two or
LESSON 3-1: Parallel Lines & Transversals d
Transversal
A line that intersects two or
more coplanar lines at two
different points 1 2 4 3 q
line d r 6 5 7 8
Transversal

10. Interior Angles <3, <4, <5, <6
LESSON 3-1: Parallel Lines & Transversals d
Interior Angles
Lie in the region between lines
q and r 1 2 4 3 q
<3, <4, <5, <6 r 6 5 7 8
Interior Angles

11. Exterior Angles <1, <2, <3, <4 Lie in the two regions not
LESSON 3-1: Parallel Lines & Transversals d
Exterior Angles
Lie in the two regions not
between lines q and r 1 2 4 3 q
<1, <2, <3, <4 r 6 5 7 8
Exterior Angles

12. Consecutive Interior Angles
LESSON 3-1: Parallel Lines & Transversals d
Consecutive Interior Angles
A pair of interior angles that
lie on the same side of
the transversal (d ) 1 2 4 3 q r
<4 & <5
<3 & <6 6 5 7 8
Consecutive Interior Angles

13. Alternate Interior Angles
LESSON 3-1: Parallel Lines & Transversals d
Alternate Interior Angles
Nonadjacent interior angles that
lie on opposite sides of
the transversal (d ) 1 2 4 3 q
<3 & <5
<4 & <6 r 6 5 7 8
Alternate Interior Angles

14. Alternate Exterior Angles
LESSON 3-1: Parallel Lines & Transversals d
Alternate Exterior Angles
Nonadjacent exterior angles that
lie on opposite sides of
the transversal (d ) 1 2 4 3 q
<1 & <7
<2 & <8 r 6 5 7 8
Alternate Exterior Angles

15. Corresponding Angles <1 & <5 ; <2 & <6
LESSON 3-1: Parallel Lines & Transversals d
Corresponding Angles
Lie on the same side of
transversal ( d ) and on the
same side of lines q and r 1 2 4 3 q
<1 & <5 ; <2 & <6
<3 & <7 ; <4 & 8 r 6 5 7 8
Corresponding Angles

16. Ex 2: Classifying Angle Pairs
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 2
Classify Angle Pair Relationships
Classify the relationship between the following angle pairs alternate interior, alternate exterior, corresponding, or consecutive interior angles.
A. 2 and 6
corresponding
B. 1 and 7
alternate exterior
C. 3 and 8
consecutive interior
D. 3 and 5
alternate interior
Ex 2: Classifying Angle Pairs

17. Ex 2: Classifying Angle Pairs
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 2
Classify Angle Pair Relationships
Classify the following relationships:
A. 4 and 5.
consecutive interior
B. 7 and 9.
corresponding
C. 4 and 7.
alternate exterior
D. 2 and 11.
alternate interior
Ex 2: Classifying Angle Pairs

18. Ex 3: ID Transversal & Angle Pairs
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 3
Identify Transversals and Classify Angle Pairs
BUS STATION The driveways at a bus station are shown. Identify the transversal connecting the angles and then classify the relationship between the pair of angles.
A. 1 and 2
line v; corresponding angles
B. 2 and 3
line v; alternate interior angles
C. 4 and 5
line y; consecutive interior angles
Ex 3: ID Transversal & Angle Pairs

19. Ex 3: ID Transversal & Angle Pairs
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 3
Identify Transversals and Classify Angle Pairs
HIKING A group of nature trails is shown. Identify the sets of lines to which the given line is a transversal:
A. line a
lines c, d, e, f
B. line b
lines c, d, e, f
C. line c
lines a, b, d, e, f
Ex 3: ID Transversal & Angle Pairs