• Identify relationships between two lines or two planes.
• Name angle pairs formed by parallel lines and transversals
Lesson 3-1: Parallel Lines & Transversals
TARGETS
Lines & Planes
LESSON 3-1: Parallel Lines & Transversals
Two lines intersect in a point
Two planes intersect in a line
A line intersects a plane at a point
Model the following situations in the items on your desk
Parallel and Skew
LESSON 3-1: Parallel Lines & Transversals
Parallel lines -
Skew lines -
Parallel planes -
Coplanar lines that DO NOT intersect
Planes that DO NOT intersect
Lines that DO NOT intersect and are not coplanar
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Plane B Plane A
Lines l and m are skew lines
Lines & Planes
LESSON 3-1: Parallel Lines & Transversals
3) Two lines are skew
2) Two planes are parallel
Model the following situations in the items on your desk
1) Two lines are parallel.
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.
Identify Parallel and Skew Relationships
AD, EH, FG
A. Name all segments parallel to BC.
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 1
B. Name a segment skew to EH.
AB, CD, BG, or CF
C. Name a plane parallel to plane ABG.plane CDE
A. Name a plane that is parallel to plane RST.
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 1 Identify Parallel and Skew Relationships
B. Name a segment that intersects YZ.
C. Name a segment that is parallel to RX.
plane WXY
WZ, XY, TS, or SY
QW, TZ, or SY
Transversal
A line that intersects two ormore coplanar lines at two different points
1
42
3
8 7
65
q
d
r
LESSON 3-1: Parallel Lines & Transversals
line d
Interior Angles
Lie in the region between linesq and r
1
42
3
8 7
65
q
d
r
LESSON 3-1: Parallel Lines & Transversals
<3, <4, <5, <6
Exterior Angles
Lie in the two regions notbetween lines q and r
1
42
3
8 7
65
q
d
r
LESSON 3-1: Parallel Lines & Transversals
<1, <2, <3, <4
Consecutive Interior Angles
A pair of interior angles that lie on the same side of
the transversal (d )
1
42
3
8 7
65
q
d
r
LESSON 3-1: Parallel Lines & Transversals
<4 & <5
<3 & <6
Alternate Interior Angles
Nonadjacent interior angles that lie on opposite sides of
the transversal (d )
1
42
3
8 7
65
q
d
r
LESSON 3-1: Parallel Lines & Transversals
<3 & <5
<4 & <6
Alternate Exterior Angles
Nonadjacent exterior angles that lie on opposite sides of
the transversal (d )
1
42
3
8 7
65
q
d
r
LESSON 3-1: Parallel Lines & Transversals
<1 & <7
<2 & <8
Corresponding Angles
Lie on the same side of transversal ( d ) and on the same side of lines q and r
1
42
3
8 7
65
q
d
r
LESSON 3-1: Parallel Lines & Transversals
<1 & <5 ; <2 & <6<3 & <7 ; <4 & 8
Classify Angle Pair Relationships
Classify the relationship between the following angle pairs alternate interior, alternate exterior, corresponding, or consecutive interior angles.
corresponding
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 2
A. 2 and 6
B. 1 and 7alternate exterior
C. 3 and 8consecutive interior
D. 3 and 5alternate interior
A. 4 and 5.
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 2 Classify Angle Pair Relationships
consecutive interior
B. 7 and 9.corresponding
C. 4 and 7.alternate exterior
D. 2 and 11.alternate interior
Classify the following relationships:
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.
LESSON 3-1: Parallel Lines & Transversals
EXAMPLE 3
A. 1 and 2
B. 2 and 3
C. 4 and 5
line v; corresponding angles
line v; alternate interior angles
line y; consecutive interior angles
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