3.2 Properties of Parallel Lines

Objectives: TSW …• Use the properties of parallel lines cut by a

transversal to determine angles measures.• Use algebra to find angle measure.

Postulate 3.1Corresponding Angles Postulate

p

m

n

1 23 4

5 687

1 5,

If a transversal intersects two parallel lines,

then corresponding angles are congruent.

2 6, 3 7, 4 8

Example 1: In the figure, x ‖ y and m10 = 120. Find m14.

Theorem 3.1:Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

p

m

n

1 23 4

5 687

4 5,3 6

Example 2: In the figure, x ‖ y and m12 = 38. Find m15.

Theorem 3.2: Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines,

then Same Side Interior Angles are supplementary.

p

m

n

1 23 4

5 687

m4 + m6 = 180, m3 + m5 = 180

Example 3: In the figure, x ‖ y and m12 = 43. Find m14.

Theorem 3.3:Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then alternate exterior angles are congruent.

p

m

n

1 23 4

5 687

1 8,2 7

Example 4: In the figure, x ‖ y and m11 = 51. Find m16.

Example 5: Finding measures of Angles

What are the measures of all numbered angles. Which theorem or postulate justifies each answer?

Example 6: What is the measure of RTV?

Example 7:If m5 = 2x – 10, m6 = 4(y – 25), and

m7 = x + 15, find x and y.

Example 8:In the figure, m3 = 110 and m12 = 55.

Find the measure of the other angles.

SummaryRelationship of angle measures formed by two

parallel lines cut by a transversal.

Corresponding Angles - congruent Alternate Interior Angles - congruent Alternate Exterior Angles - congruent Same Side Interior Angles - Supplementary