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Stand
Quietly
Lesson 3.1 Parallel
Lines and Transversals
Students will be able to describe
angles formed by parallel lines and
transversals
Warm-Up #37 1/4/17
1. What is the volume of a cylinder given the
diameter of 10 inches and the height of 2
inches?
2. Find the new point for (3,6) given
(x,y) (x-4, y+5). What type of
transformation is this?
3. Find the new point for (3,6) given
(x,y)  (2x, 2y). What type of transformation
is this?
Homework 1/4/17
Textbook page 107
#3-6, 25, 31-35
Homework Solutions
Homework 1/5/17
Worksheet: 3.1 Practice A
Answer these questions in your notebook:
1) What does it mean for two lines to be
parallel? What are some properties of two
parallel lines?
2) Write a strategy for drawing two parallel lines.
When an object is transverse, it is lying or
extending across something.
2
1
3
4
5
6
7
8
Transversal line
1. How many angles are formed by the parallel lines
and the transversal? Label the angles.
2. Which of these angles have equal measures?
Explain your reasoning.
Transversal: a line that intersect
two or more lines. When parallel
lines are cut by a transversal,
several pairs of congruent angles
are formed.
The measurement of a straight line is
180 degrees.
PROPERTIES OF PARALLEL LINES
POSTULATE
POSTULATE 15 Corresponding Angles Postulate
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles
are congruent.
1
2
1
2 Because of the
corresponding angles
postulate
1
3
2
4
7
5
8
6
PROPERTIES OF PARALLEL LINES
THEOREMS ABOUT PARALLEL LINES
THEOREM 3.4 Alternate Interior Angles
If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are
congruent.
3
4
3
4
Because of the
alternate interior angles
postulate
PROPERTIES OF PARALLEL LINES
THEOREMS ABOUT PARALLEL LINES
THEOREM 3.6 Alternate Exterior Angles
If two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles are
congruent.
7
8
7
8
Because of the
alternate exterior
angles postulate
PROPERTIES OF PARALLEL LINES
THEOREMS ABOUT PARALLEL LINES
THEOREM 3.7 Perpendicular Transversal
If a transversal is perpendicular to one of two parallel
lines, then it is perpendicular to the other.
j
k
Key Concepts
• Angles can be labeled with one point at the vertex,
three points with the vertex point in the middle, or with
numbers. See the examples that follow.
18
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Adjacent angles
∠ABC is adjacent to
∠CBD. They share vertex
B and
.
∠ABC and ∠CBD have no
common interior points.
19
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Nonadjacent angles
∠ABE is not adjacent to ∠FCD.
They do not have a common vertex.
(continued)
20
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Nonadjacent angles
∠PQS is not adjacent to ∠PQR. They share common
interior points within ∠PQS.
21
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Linear pair
∠ABC and ∠CBD are a
linear pair. They are
adjacent angles with
non-shared sides,
creating a straight angle.
22
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Not a linear pair
∠ABE and ∠FCD are not
a linear pair. They are not
adjacent angles.
23
1.8.1: Proving the Vertical Angles Theorem
Vertical angles are nonadjacent
angles formed by two pairs of
opposite rays. Opposite angles are
congruent to each other.
24
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Vertical angles
∠ABC and ∠EBD are
vertical angles. ÐABC @ ÐEBD
∠ABE and ∠CBD are
vertical angles. ÐABE @ ÐCBD
25
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Not vertical angles
∠ABC and ∠EBD are not vertical angles.
and
are
not opposite rays. They do not form one straight line.
26
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
Theorem
Supplementary Theorem
If two angles add up to be 180 degrees,
then they are supplementary.
27
1.8.1: Proving the Vertical Angles Theorem
Key Concepts, continued
• Complementary angles are two angles
whose sum is 90º. Complementary
angles can form a right angle or be
nonadjacent.
28
1.8.1: Proving the Vertical Angles Theorem