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

2. Mathematical Practices
Content Standards
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
CCSS

3. Lines & Planes (modeling)
LESSON 3-1: Parallel Lines & Transversals
Lines & Planes
Two lines intersect in a
point
A line intersects a plane at a
point and a line
Two planes intersect in a
line
Lines & Planes (modeling)

4. Parallel and Skew Parallel lines - Coplanar lines that DON’T intersect
Parallel planes -
Planes that DON’T intersect
Plane A
Plane B
Skew lines -
NOT Parallel
DON’T Intersect
NOT Coplanar
Lines a and f are skew lines
Parallel & Skew

5. A. Name a plane that is parallel to plane RST.
A. plane WTZ
B. plane SYZ
C. plane WXY
D. plane QRX
Example 1a

6. 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

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

8. Parallel Lines and Transversals
Two lines divide the plane into three regions.
The region between the lines is referred to as the interior.
The two regions not between the lines is referred to as the exterior.
Exterior
Interior

9. b l m c t r Definition of Transversal
In a plane, a line is a transversal iff it intersects two or more
Lines, each at a different point.
The lines cut by a transversal may or may not be parallel. l m 1 2 3 4 5 7 6 8
Parallel Lines
t is a transversal for l and m. t 1 2 3 4 5 7 6 8 b c
Nonparallel Lines
r is a transversal for b and c. r

10. When a transversal intersects two lines, _____ angles are formed.
eight
These angles are given special names. l m 1 2 3 4 5 7 6 8 t
Interior angles lie between the
two lines.
Exterior angles lie outside the
two lines.
Alternate Interior angles are on the
opposite sides of the transversal.
Alternate Exterior angles are
on the opposite sides of the
transversal.
Consectutive Interior angles are on the same side of the transversal. ?

11. LESSON 3-1: Parallel Lines & Transversalsd
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

12. 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

13. 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

14. 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

15. HOMEWORK
Pgs
#’s 1-12, 15, 21-30, 38-43,
51, 55-58