do now a b c d 1.name a line that does not intersect with line ac. 2.what is the intersection of...
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Parallel Lines Lines that do not Intersect and are coplanarTRANSCRIPT
Do Now
A B
C D1. Name a line that does not intersect with
line AC. 2. What is the intersection of lines AB and
DB?
3.1 Identify Pairs of Lines and Angles
3.2 Use Parallel Lines and Transversals
Objective: To identify angle pairs formed by three intersecting lines; to
use angles formed by parallel lines and transversals
Parallel Lines
Lines that do not Intersectand arecoplanar
Parallel Planes
Planes thatDo notIntersect
Skew Lines
Lines that doNot intersectand are notCoplanar.
Transversal
• Transversal: a line that intersects two or more coplanar lines.
Angles formed by a transversal
• There are 4 types of angles formed by a transversal.
Corresponding angles1
5
Angles 1 and 5 are correspondingBecause they have correspondingPositions.
Corresponding angles of Parallel Lines1
5
The corresponding angles 1 and 5 Are congruent to each other Because lines k and m are parallelTo each other.
k
m
Alternate Exterior Angles1
Angles 1 and 8 are alternate Exterior angles because they areOn alternate sides of the Transversal and are exteriorOf the two lines.
8
Alternate Exterior angles of Parallel Lines
1
The alternate exterior angles 1 and 8 are congruent to each other because lines k and m are Parallel to each other.
k
m 8
Alternate Interior Angles
Angles 3 and 6 are alternate interior angles because they areOn alternate sides of the Transversal and on the interiorOf the two lines.
3
6
Alternate Interior angles of Parallel Lines
The alternate interior angles 3 and 6 are congruent to each other because lines k and m are Parallel to each other.
k
m6
3
Consecutive Interior Angles
Angles 4 and 6 are consecutiveInterior angles because they areOn the same side of the transversalAnd are inside the two lines.
4
6
Consecutive Interior angles of Parallel Lines
The consecutive interior angles 4 and 6 are supplementary to each other because lines k and m are parallel to each other.
k
m6
4
Parallel lines cut by a transversal.
• When two parallel lines are cut by a transversal the following relationships are true.– Corresponding angles are congruent– Alternate exterior angles are congruent– Alternate interior angles are congruent– Consecutive interior angles are
supplementary.
Example 1:1
5
Name all pairs of corrsponding, alternate interior, alternate exterior, and consecutive interior angles.
23 4
67 8
Example: Classify the angle pair
x
y
Example: Classify the angle pair
m
n
Example: Classify the angle pair
p
q
Example 2: Solve for the variable
2p
120
Example 3: Solve for the variable
x
80
Example 4: Find all the missing angle measures
105