3-2 Angles and Parallel Lines3-2 Angles and Parallel Linespage 180page 180

PROPERTIES OF PARALLEL LINES

POSTULATE

POSTULATE 15 Corresponding Angles Postulate

1

2

1 2

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

PROPERTIES OF PARALLEL LINES

THEOREMS ABOUT PARALLEL LINES

THEOREM 3.4 Alternate Interior Angles

3

4

3 4

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

PROPERTIES OF PARALLEL LINES

THEOREMS ABOUT PARALLEL LINES

THEOREM 3.5 Consecutive Interior Angles

5

6

m 5 + m 6 = 180°

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

PROPERTIES OF PARALLEL LINES

THEOREMS ABOUT PARALLEL LINES

THEOREM 3.6 Alternate Exterior Angles

7

8

7 8

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

PROPERTIES OF PARALLEL LINES

THEOREMS ABOUT PARALLEL LINES

THEOREM 3.7 Perpendicular Transversal

j k

If a transversal is perpendicular to one of two parallellines, then it is perpendicular to the other.

Proving the Alternate Interior Angles Theorem

Prove the Alternate Interior Angles Theorem.

SOLUTION

GIVEN p || q

p || q Given

Statements Reasons

1

2

3

4

PROVE 1 2

1 3 Corresponding Angles Postulate

3 2 Vertical Angles Theorem

1 2 Transitive property of Congruence

Using Properties of Parallel Lines

SOLUTION

Given that m 5 = 65°, find each measure. Tellwhich postulate or theoremyou use.

Linear Pair Postulatem 7 = 180° – m 5 = 115°

Alternate Exterior Angles Theoremm 9 = m 7 = 115°

Corresponding Angles Postulatem 8 = m 5 = 65°

m 6 = m 5 = 65° Vertical Angles Theorem

Using Properties of Parallel Lines

Use properties ofparallel lines to findthe value of x.

SOLUTION

Corresponding Angles Postulatem 4 = 125°

Linear Pair Postulatem 4 + (x + 15)° = 180°

Substitute.125° + (x + 15)° = 180°

PROPERTIES OF SPECIAL PAIRS OF ANGLES

Subtract.x = 40°

Ex. 2 Find the values of x, y, and z

• MA //HT and NG//EL• 2x = 72• X = 36• 5y + 2 = 72• 5y = 70• Y = 14• 4z + 72 = 180• 4z = 108• Z = 27

4z 2x

72

5y+2

NE

M A

H T

G L

Given p//q , m<1 =107, and m<11 Given p//q , m<1 =107, and m<11 = 48. Find the measure of each = 48. Find the measure of each angle.angle.

1

11

pq

Find x and y.Find x and y.

4x-53y+1

3x+11

Find x and y.Find x and y.

• Given that a//b, find x and y.

6y 9x+12

13y-10

a

b

• Class work on page 183 problems 1-10

• Homework on page 183 problems 11-29