Download Geometry 3-2 Angles and Parallel Lines A. Parallel lines and angle

Geometry 3-2 Angles and Parallel Lines
A. Parallel lines and angle pairs
1
1. Corresponding Angles Postulate – If 2 parallel
lines are cut by a ____________, then each pair of
corresponding angles is congruent.
∠ 1 ≅ ∠ 5, ∠ 2 ≅ ∠ 6, ∠ 3 ≅ ∠ 7, ∠ 4 ≅ ∠ 8
2
1
3
5
6
4
l
Example 1: If l m, and m ∠ 1 = 142,
Find m ∠ 8.
1
2
1
m
5
3
4
l
t
7
8
6
t
7
8
m
2. Theorem 3-1 – Alternate Interior Angles Theorem – If two parallel lines
are cut by a transversal, then each pair of alternate interior angles is
congruent. So- m ∠ ___ ≅ m ∠ ___ and m ∠ ___ ≅ m ∠ ___
3. Theorem 3-2 – Consecutive Interior Angles Theorem – If two parallel
lines are cut by a transversal, then each pair of consecutive interior angles
is supplementary. So - m ∠ ___ + m ∠ ___ = ___° and
m ∠ ___ + m ∠ ___ = ___°
4. Theorem 3-3 – Alternate Exterior Angles Theorem – If two parallel lines
are cut by a transversal, then each pair of alternate exterior angles is
congruent. m ∠ ___ ≅ m ∠ ___ and m ∠ ___ ≅ m ∠ ___
5. Theorem 3-4 – Perpendicular Transversal Theorem – In a plane, if a line is
perpendicular to one of two parallel lines, then it is perpendicular to the
other.
Example 2: p q and t is a transversal,
a)
b)
c)
d)
Find m ∠ 1 if m ∠ 3 = 50
Find m ∠ 4 if m ∠ 5 = 145
Find m ∠ 2 if m ∠ 7 = 30
Find m ∠ 8 if m ∠ 2 = 40
p
1
2
3
41
6
5 7
8
q
t
Example 3: In the figure, MA HT and NG
y, z, and the measure of ∠ NMR
EL , find the values of x,
x = ___
y = ___
N
R
E
A
M
4z
2x
z = ___
m ∠ NMR = ___
O
H
T 72
(5 y + 2)
G
Geometry HW: Section 3-2 p. 136-138
14-36 all, 39, 45-46, 47-59 odd
L
C