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Parallel Lines and Plan Dallas City Hall I.M. Pei Parthenon Athens Havasu Falls I.M. Pei Lesson 3.2 Classroom Exercises
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Parallel Lines and Planes
Dallas City HallI.M. Pei
ParthenonAthens
Havasu FallsI.M. Pei
Lesson 3.2 Classroom Exercises
Mr. Sabia’s Favorite Theorem
Vertical angles are congruent.VA are
X marks the spot.
Mr. Sabia’s 2nd Favorite TheoremLinear pairs are supplementary.
Lp’s are suppl.
a b
180m a m b
Mr. Sabia’s Third Favorite TheoremIf 2 lines are //, then the Alternate Interior angles are congruent.
AIA are
If two lines are parallel….
The corresponding angles are congruent.
The alternate interior angles are congruent.
The alternate exterior angles are congruent.
The same-side interior angles are supplementary.
The same-side exterior angles are supplementary.
87
65
43
21L
P
1
What do the arrowheads in the diagram tell you?
L // P
KT
87
65
43
21L
P
2 State the postulate or theorem that justifies each statement.
1 5
If 2 lines are parallel and cut by a transversal,Then the corresponding angles are congruent.
KT
87
65
43
21
3 6
L
P
3 State the postulate or theorem that justifies each statement.
If 2 lines are parallel and cut by a transversal,Then the alternate interior angles are congruent.
KT
L
P
4 State the postulate or theorem that justifies each statement.
If 2 lines are parallel and cut by a transversal,Then the same-side interior angles are supplementary.
4 6 180m m 87
65
43
21
KT
L
P
5 State the postulate or theorem that justifies each statement.
If 2 lines are parallel and cut by a transversal,Then the corresponding angles are congruent.
4 8m m 87
65
43
21
KT
L
P
6 State the postulate or theorem that justifies each statement.
If 2 lines are parallel and cut by a transversal,Then the alternate interior angles are congruent.
4 5m m
KT
87
65
43
21
L
P
7 State the postulate or theorem that justifies each statement.
Vertical angles are congruent.
KT
6 7 87
65
43
21
87
65
43
21L
P
8 State the postulate or theorem that justifies each statement.
If a line is perpendicular to on of two parallel lines, then it is perpendicular to the other.
K P
KT
L
P
9 State the postulate or theorem that justifies each statement.
KT
3 5is complementary to
If 2 lines are parallel and cut by a transversal,Then the same-side interior angles are supplementary.
87
65
43
21
87
65
43
21L
P
10 State the postulate or theorem that justifies each statement.
KT
If the measure of angle 1 is 130, what are the measures of the other angles?
1300
1300
1300
1300
500
500
500
500
87
65
43
21L
P
11 State the postulate or theorem that justifies each statement.
KT
If the measure of angle 1 is x, what are the measures of the other angles?
x
x
x
x
180-x
180-x
180-x
180-x
87
65
43
21L
P
12 State the postulate or theorem that justifies each statement.
KT
4 2 3,
6.
If m m
then find m
x 2x
x + 2x = 180
3x = 180
x = 60
60, AIA
L
P
13 State the postulate or theorem that justifies each statement.
KT
5 6 20,
1.
If m m
then find m
xx + 20
x + x + 20 = 180
2x + 20 = 180
x = 80
CA
2x = 1601 20m x
1 100m
87
65
43
21
C’est fini.
Good day and good luck.
