DO NOW - Geometry
**Draw the figure.
Given: line a and line b are parallel.
The measure of angle 1 is 105
a
b
Find: the measures of angles 2,3,4,5,6,7 and 8.
Identify: the transverse line.
c
S
Vocabulary
S In your notebook/binder write the definitions for the
following terms:
S parallel lines
parallel planes
S skew lines
transversal
S consecutive interior
angles
S alternate exterior angles
alternate interior angles
S corresponding angles
3.1: Parallel Lines and
Transversals
Chapter 3: Angles and Triangles
S
Recall?
S || means two lines are parallel
S | means two lines are perpendicular
S || means two lines are NOT parallel
What is a Transversal?
S
Lines in the same plane that do not
intersect are called parallel lines.
S
Lines that intersect at rights angles
are called perpendicular lines.
S
Transversal- a line that intersects
two or more lines.
S
When parallel lines are cut by a
transversal, several pairs of
congruent angles are formed.
Question
S What does corresponding mean?
(take a moment to really consider the
definition before we move forward)
S (write the answer in your notes)
Corresponding Angles
S
When a transversal intersects
parallel lines, corresponding
angles are congruent.
Finding Angle Measures
Use the figure to find the measures of (a) <1 and (b) <2.
S
(a) <1 and the 110 degree angles
are corresponding angles. They
are congruent
S So, the measure of <1 is 110
S
<1 and <2 are supplementary,
The sum of the angles is 180
degrees.
 1  2  180 0
110 0   2  180 0
 2  70 0
Practice
Use the figure to find the measure of <1 and <2. explain your reasoning.
S
<1 and 63 degrees are
corresponding angles, sot <1 is
63 degrees.
S
<1 and <2 are supplementary
angles.
 1  2  1800
630   2  1800
 2  117 0
Using Corresponding Angles
Use the figure to find the measures of the numbered angles.
S
<1 and the 75 degree angle are
vertical angles, so they are
congruent.
S So, <1=75
S
The 75 degree angle is supplementary
to both <2 and <3.
75 0   2  180 0
S
 2  105 0
So, the measures of <2 and <3 are
105
Using corresponding angles, the measures
 of <4 and<6 are 75, and the
measures of <5 and <7 are 105.
Practice
S
Use the figure to find the
measure of the numbered angles.
 1  1210
 2  590
 3  1210
 4  1210
 5  590
 6  1210
 7  590
Interior and Exterior Angles
S
When two parallel lines are cut by
a transversal:
S Four interior angles are
formed on the inside of the
parallel lines.
S Four exterior angles are
formed on the outside of the
parallel lines.
S
<3, <4, <5, and <6 are interior
angles.
S
<1, <2, <7, and <8 are exterior
angles.
Using Corresponding Angles
S
A store owner uses pieces of tape
to paint a window advertisement.
The letters are slanted at an 80
degree angle. What is the
measure of <1?
S
Because all the letters are slanted at an
80 degree angle, the dashed lines are
parallel. The pieces of tape is the
transversal.
S Using corresponding angles, the 80
degree angle is congruent to the
angle that is supplementary to <1.
The measure of <1 is 180-80=100 degrees.
Question
What does exterior mean?
What does interior mean?
S
Alternate Interior and Alternate
Exterior Angles
S
When a transversal intersects
parallel lines
S Alternate interior angles are
congruent
S Alternate exterior angles are
congruent
Identifying Alternate Interior
and Alternate Exterior Angles
The photo shows a portion of an airport. Describe the relationship
between each pair of angles.
S
<3 and <6 are alternate exterior
angles.
S <3 is congruent to <6
S
<2 and <7 are alternate interior
angles.
S <2 is congruent to <7
Assignment
S Pg 136-137 #14-36 (evens)