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

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43

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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

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21L

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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

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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

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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

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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

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C’est fini.

Good day and good luck.