Download Special Angles on Parallel lines

Angle Relationships and Special
Angles on Parallel lines
Objective: Students will be able to
apply definitions of angles to determine
missing angle measurements.
Linear Pair – adjacent angles that are
supplementary
Adjacent angles – two angles that have the
same vertex and share a side
Vertical Angles – angles formed by intersecting
lines, opposite each other, share vertex but no
sides, they are congruent
Given the picture prove why angle 1 and 3 are
congruent without using vertical angles.
(deductive reasoning)
2
3
4
1
Statement
<1+<2=180
<2+<3=180
<1+<2=<2+<3
<1=<3
Reason
Linear Pair
Linear Pair
Substitution
Subtraction
Angle 1 and 2 are a linear as are 2 and 3. Since
both are linear pairs both equal 180 therefore are
equal to each other. Angle 2 is common in both
and can be removed therefore angle 1 is equal to
angle 3
Relationships of Lines
Parallel lines – lines that never touch, have same
slope
symbol = ||
Perpendicular lines – lines that intersect and
form right angles, slopes are opposite
reciprocals
symbol = 
Parallel Lines and a Transversal
Transversal – line that intersects two or more
lines at different points
There are relationships between some of the
angles, if the lines the transversal crosses are
parallel then there are more properties
Need to state lines are parallel
do not assume that they are,
symbol for parallel lines both
have an arrow on line.
Interior Angles – angles that are between the
two lines that the transversal crosses
Exterior Angles – angles outside the two lines
that the transversal crosses
Exterior
Interior
Exterior
4 Main properties with Parallel lines
and Transversals
Corresponding Angles
Same side of transversal, nonadjacent,
one interior and one exterior, congruent if
lines are parallel
Alternate Interior Angles
Both interior angles, opposite sides of
transversal, nonadjacent, congruent in
lines are parallel
Alternate Exterior Angles
Both exterior, opposite sides of the
transversal, nonadjacent, congruent if
lines are parallel
Same Side Interior Angles
Both Interior, same side of the
transversal, supplementary if lines
are parallel
Transversal
Exterior
2
1
4
3
Interior
5
7
6
8
Exterior
110
3
k
1
2
names
of lines
4
7
5
l
6
Lines are parallel
Backward Properties
Know that the reverse of the properties can be
true.
If corresponding angles are congruent then the
lines are parallel.
If alternate interior angles are congruent then
the lines are parallel.
Objective: Students will be able to apply
definitions of angles to determine missing angle
measurements.
On a scale of 1 to 4 Do you feel we meet the
objective for the day.
If we did not meet the objective, what did we
miss and how could I improve.
Homework
Pg 124
4,6,8
Pg 131
1-5 odd, 9 and 10
Honors pg 132 7