Download Alternate Interior Angles

Parallel lines and Transversals
Sec 3.1
Sol:G.3a
Parallel Lines
• Parallel lines are coplanar lines that do not intersect.
• Arrows are used to indicate lines are parallel.
• The symbol used for parallel lines is ||.
A
C
B
D
In the above figure, the arrows show that line AB is parallel to
line CD.
With symbols we denote, AB CD .
Lesson 2-3: Pairs of Lines
3
OBLIQUE LINES
• Oblique lines are lines that intersect, but do NOT form
a right angle.
• m  n
Lesson 2-3: Pairs of Lines
4
Skew Lines and Parallel Planes
Definition: Skew lines are lines that are noncoplaner and do not intersect.
Ex: What lines are skew to AE ?
Definition: Parallel planes are
planes that do not intersect.
Ex : Name a set of parallel planes.
Example
Transversal
• Definition: A line that intersects two or more lines in a plane
at different points is called a transversal.
Note: Transversals intersects do not always have to be Parallel.
• When a transversal t intersects line n and m, eight angles of
the following types are formed:
t
m
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles
n
Lesson 2-4: Angles and Parallel Lines
7
Exterior and Interior Angles
Exterior Angles: Angles that are on the “outside”
of the two “clusters”
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Interior Angles: Angles that are in the “middle “
of the two “clusters”
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Consecutive Interior Angles
Consecutive Interior Angles: (Same-side Interior
Angles)
Are on the same side of the transversal.
On the inside.
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Alternate Exterior and Alternate
Interior Angles
Alternate Exterior Angles:
Are on the opposite sides (or they alternate
sides) of the transversal.
Are on the outside.
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Alternate Interior Angles:
Are on the opposite sides of the transversal.
Are on the inside.
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Corresponding Angles
Corresponding Angles:
Occupy the same place in the different clusters.
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m
l
1 8
10 2
t
5
11
7
4
12
6
3 9
1. Identify each pair of angles as Alt. interior, Alt. exterior, Corresponding or
Consecutive interior angles.
a. 6and10
b. 9and11
c. 1and5
d. 3and8
e. 7and12
f. 4and8
2. Identify all pairs of vertical angles.
3. Identify all linear pairs.
Assignment
Hw: pg 128-129 22-27, 32-39 and 49-51
Angles and Parallel Lines
Section 3.2
Sol: G.3a, c, f
E.Q.: Compare and contrast parallel lines with a
transversal and non-parallel lines and a transversal.
Angles and Parallel Lines
•
1.
2.
3.
•
1.
2.
If two parallel lines are cut by a transversal, then the
following pairs of angles are congruent.
Corresponding angles
Alternate interior angles
Alternate exterior angles
If two parallel lines are cut by a transversal, then the
following pairs of angles are supplementary.
Consecutive interior angles
Consecutive exterior angles
Continued…..
Lesson 2-4: Angles and Parallel Lines
15
3-1 Corresponding angles postulate
• If two parallel lines are cut by a transversal, then each
pair of corresponding angles are congruent.
 2   6,  1   5,  3   7,  4   8
1
3
5
7
2
4
6
8
Lesson 2-4: Angles and Parallel Lines
16
3-2 Consecutive Interior Angles Theroem
If two parallel lines are cut by a transversal, then then each pair of
consecutive interior angles is supplementary.
m3 +m5 = 180º, m4 +m6 = 180º
1
3
5
7
Lesson 2-4: Angles and Parallel Lines
2
4
6
8
17
Alternate Angles
• 3-1 Alternate Interior Angles Thereom: If two parallel lines are
cut by a transversal, then each pair of alternate interior angles are
 3   6,  4   5
Congruent.
• 3-3 Alternate Exterior Angles: If two parallel lines are cut by a
transversal, then each pair of alternate exterior angles are
Congruent.
 2   7,  1   8
1
3
5
7
2
4
6
8
Lesson 2-4: Angles and Parallel Lines
18
3-4 Perpendicular Transversal Thereom
• In a plane, if a line is perpendicular to one or more parallel
lines, then it is perpendicular to the other.
l
m
b
• l||m and a||b
a
Assignments
Homework: Handout