Download 10-1 Line and Angle Relationships

10-1 Line and Angle Relationships
Parallel lines –two lines that never intersect.
a llb
line a is parallel to line b
a
b
When two parallel lines are intersected by a third line called a transversal, eight angles are
formed.
a llb (states: line a is parallel to line b)
line m is the transversal.
m
a
1
2
**for each vocab word refer to this diagram
3 4
b
5 6
7 8
Interior angles lie inside the parallel lines. <3,<4, <5, <6
Exterior angles lie outside the parallel lines. <1,<2, <7, <8
Alternate interior angles are opposite sides of the transversal & inside the parallel lines.
Angles are congruent to one another. Ex: if you know the measure of one, you know the
measure of the other.
EX: <3 & <6; <4 & <5
Alternate exterior angles are opposite sides of the transversal and outside the parallel
lines. Angles are congruent to one another. Ex: if you know the measure of one, you
know the measure of the other.
EX: <1 & <8;
<2 & <7
Corresponding angles are in the same spot on the other parallel line. Angles are congruent
to one another. Ex: if you know the measure of one, you know the measure of the other.
EX: <1 & <5; <2 & <6;
<3 & <7;
<4 & <8
Vertical angles two pairs of opposite angles formed from 2 intersecting lines. Angles are
congruent to one another. Ex: if you know the measure of one, you know the measure of
the other.
EX: <1&<4: <2&<3; <5&<8;
<6&<7
Adjacent angles – two angles have the same vertex, share a common side, and do not
overlap.
EX: <1 & <2 are adjacent angles
**Nothing to do with size/measure
•b
a•
1 2
c
Complementary – two angles in which the sum measures 90º
<1 is complimentary to <2; m<1 + m<2 = 90º
(m means “the measure of..”)
1
2
Supplementary – two angles in which the sum measures 180º
<1 is supplementary to <2; m<1 + m<2 = 180º
1
2
Perpendicular lines – lines that intersect to form a right angle
a
b
Line a is perpendicular to line b;
a
b
Example #1
allb and m is a transversal. If m<1 = 68º, find the measure of the remaining angles. *you
can write the measures right inside this diagram
m
68° 1 2
3 4
a
5
b
6
7 8
Example #2
allb and m is a transversal. If m<2 = 123º, find the measure of the remaining angles.
m
1 2 123º
3 4
a
5
b
6
7 8
Example #3
allb and m is a transversal. If m<6 = 116º, find the measure of the remaining angles.
m
1 2
3 4
a
5 6 116º
7 8
b
Example #4
allb and m is a transversal. If m<8 = 43º, find the measure of the remaining angles.
m
1 2
3 4
a
5 6
7 8
b
7 8