Download Geometry 3-5 Proving Lines Parallel A. Identify Parallel Lines 1

Geometry 3-5 Proving Lines Parallel
A. Identify Parallel Lines
1. Postulate 3-4 – If two lines in a plane are cut by a transversal so that
_____________ angles are congruent, then the lines are _______________.
Abbreviation – If corr ∠ ’s are ≅ , then they are .
If ∠ 3 ≅ ∠ 7, then _____________
1 3
2 4
5
6
7
8
t
m
l
2. Postulate 3-5 – If given a line and a point not on the same line, then there
exists _______________ line through the point that is parallel to the given
line.
3. Theorem 3-5 – If two lines in a plane are cut by a transversal so that a pair of
alternate exterior angles is congruent, then the two lines are parallel.
Abbreviation: If alt. ext. ∠ ’s are ≅ , then the lines are .
If ∠ 1 ≅ ∠ 8, then ____________
4. Theorem 3-6 – If two lines in a plane are are cut by a transversal so that a pair
of consecutive interior angles is supplementary, then the two lines are parallel.
Abbreviation: If cons. Int. ∠ ’s are suppl., then the lines are .
If m ∠ 4 + m ∠ 6 = 180 ° , then ____________
5. Theorem 3-7 – If two lines in a plane are cut by a transversal so that a pair of
alternate interior angles is congruent, then the two lines are parallel.
Abbreviation: If alt. int. ∠ ’s are ≅ , then the lines are .
If ∠ 4 ≅ ∠ 5, then ____________
6. In a plane, if two lines are perpendicular to the same line, then they are
parallel.
Abbreviation: If 2 lines are ⊥ to the same line, then the lines are .
If a ⊥ t, and b ⊥ t, then _________
a
b
t
Example 1: Determine which lines if any are parallel.
103 °
77 °
102 °
Example 2: Find x and m ∠ ZYN, so that PQ MN .
W
11x - 25 °
X
P
Q
Y
7x + 35 °
M
Z
Geometry HW: 3-5 p. 155-157
14-30 even, 34-35, 38-39, 47-55 odd, 61-63
N