3.2

Use Parallel Lines and Transversals

Essential Question

How are corresponding angles and alternate interior angles related for two parallel lines and a transversal?

M11.B.2.1,M11.B.2.2, M11.C.1.2, M11.C.3.11

More Postulates and Theorems

Which angle pairs have the same angle measure by the Corresponding Angle

Postulate?

<a & <e, <b & <f, <c & <g, <d & <h

What angle pairs are congruent according to the Alternate Interior Angles Theorem?

<c & <f, <d & <e

Which angle pairs are congruent according to the Alternate Exterior Angle

Theorem?

<a & <h, <b & <g

Which angle pairs are supplementary according to the Consecutive Interior

Angles Theorem?

<c & <e, <d & <f

How can you find the value for x?

3x – 10 = 140

3x = 150

x = 50

How would you find the value for x?

By the Consecutive Interior Angles Theorem we know that the sum of these angles is 180.

113 + 2x – 25 = 180

2x + 88 = 180

2x = 92

x = 46

How would you find the value for x?

3x + 2 + x + 2 = 1804x + 4 = 180

4x = 176

x = 44

Consecutive Interior Angles

The 90˚ angle and the 2x˚ angle are Consecutive Interior angles so we know they are supplementary, so their sum is 180˚

90 + 2x = 180

2x = 90

x = 45

The 6y˚ angle and the 3y˚ angle are Consecutive Interior angles so we know they are supplementary, so their sum is 180˚

6y + 3y = 180

9y = 180

y = 20