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Parallel Lines and Transversals In geometry, a line, line segment, or ray that intersects two or more lines at different points is called a __________ transversal l m B A is an example of a transversal. It intercepts lines l and m. Note all of the different angles formed at the points of intersection
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• 9/29/15• Unit 2: Parallel Lines• Aim: Students will be able to identify relationships
between angles formed by two parallel lines cut by a transversal
• Homework: • Do Now: Solve for x and y
Parallel Lines and Transversals
You will learn to identify the relationships among pairs of interior and exterior angles formed by two parallel linesand a transversal.
Parallel Lines and Transversals
In geometry, a line, line segment, or ray that intersects two or more lines at different points is called a __________transversal
l
m
B
A
AB is an example of a transversal. It intercepts lines l and m.
Note all of the different angles formed at the points of intersection.
1 234
57
68
Parallel Lines and Transversals
Definition ofTransversal
In a plane, a line is a transversal if it intersects two or morelines, each at a different point.
The lines cut by a transversal may or may not be parallel.
l m
1 234
576
8
ml
Parallel Lines
t is a transversal for l and m.
t
1 234
57
68
b
ccb ||
Nonparallel Lines
r is a transversal for b and c.
r
Parallel Lines and TransversalsTwo 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
Exterior
Interior
l m
1 234
576
8
Parallel Lines and Transversals
When a transversal intersects two lines, _____ angles are formed.eightThese angles are given special names.
t
Interior angles lie between thetwo lines.
Exterior angles lie outside thetwo lines.
Alternate Interior angles are on the opposite sides of the transversal,between the lines.Same Side Interior angles are on the same side of the transversal, between the lines.
Alternate Exterior angles areon the opposite sides of thetransversal, outside the lines.Same Side Exterior angles are on the same side of the transversal , outside the lines.
Alternate angles lie on opposite sides of the transversal
Same Side angles lie on the sameside of the transversal
Parallel Lines and Transversals
AlternateInteriorAngles
AIA
If two parallel lines are cut by a transversal, then each pair ofAlternate interior angles is _________.
1 234
57
68
64 53
congruent
Parallel Lines and Transversals
1 234
576
8
Same SideInteriorAngles
SSI
If two parallel lines are cut by a transversal, then each pair ofSame side interior angles is _____________.supplementary
18054 18063
Same SideExteriorAngles
SSE
If two parallel lines are cut by a transversal, then each pair ofSame side exterior angles is _____________.
Parallel Lines and Transversals
1 234
576
8
supplementary
18081 18072
Parallel Lines and Transversals
1 234
576
8
AlternateExteriorAngles
AEA
If two parallel lines are cut by a transversal, then each pair ofalternate exterior angles is _________.congruent
71 82
CorrespondingAngles
CA
If two parallel lines are cut by a transversal, then each pair ofcorresponding angles is _________.
congruent
Parallel Lines and Transversals
Parallel Lines w/a transversal AND Angle Pair Relationships
ConceptSummary
Congruent Supplementary
alternate interior angles- AIA
alternate exterior angles- AEA
corresponding angles - CA
same side interior angles- SSI
Types of angle pairs formed when a transversal cuts two parallel lines.
vertical angles- VAlinear pair of angles- LP
same side exterior angles- SSE
s t
c
d
1 2 3 45 6 7 8
9 10 11 1213 14 15 16
s || t and c || d.
Name all the angles that are congruent to 1.Give a reason for each answer.
3 1 corresponding angles
6 1 vertical angles
8 1 alternate exterior angles
9 1 corresponding angles
1 4 same side exterior angles
14 1 alternate exterior angles
5 10 alternate interior angles
Parallel Lines and Transversals
Let’s Practicem<1=120°Find all the remaining angle
measures.1
4
2
65
7 8
3
60°
60°
60°
60°
120° 120°
120°
120°
Parallel Lines and Transversals
Another practice problem
Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.
40°
120°
120°60°
60°
40°60°
60°180-(40+60)= 80°
80°
80°
80°
100°
100°
Parallel Lines and Transversals
Lesson 2-4: Angles and Parallel Lines 16
Example:
1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.
If line AB is parallel to line CD and s is parallel to t, find:
2. the value of x, if m<1 = 100 and m<8 = 2x + 10.
3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20.
ANSWERS:
t
16 151413
12 11109
8 765
3421
s
DC
BA1. 30
2. 35
3. 33
