3.2 - Parallel Lines and Transversals

3.2 - Parallel Lines and Transversals

​Objective:

​

To use properties of parallel lines to find angle measures.​

​

​Last time...

​We gave names to the angle pairs created when two lines are cut by a transversal.

​Do you remember them?

​Do you remember them?

​Alternate

Interior Angles​

​Do you remember them?

​Alternate

Exterior Angles​

​Do you remember them?

​Corresponding Angles​

​Do you remember them?

​Consecutive

Interior Angles​

​Do you remember them?

​Consecutive

Exterior Angles​

​Do you remember them?

​Vertical

Angles​

​Today...

​If we explore the specific case of two parallel lines cut by a transversal, we find that the angle measures have certain relationships.

​And a couple of theorems:

​

​The full list:

• ​Corresponding Angles are congruent

• ​Alternate Interior Angles are congruent

• ​Alternate Exterior Angles are congruent

• ​Consecutive Interior Angles are supplementary

• ​Consecutive Exterior Angles are supplementary

​

Previously we had learned that:

• vertical angles are always congruent

• angles that form a linear pair are always supplementary

Multiple Choice

$$\angle4$$   and  $$\angle6$$  are:

• Supplementary by the Vertical Angles Theorem

• Congruent by the Alternate Interior Angles Theorem

• Supplementary by the Alternate Exterior Angles Theorem

• Congruent because they are a linear pair

Multiple Choice

$$\angle2$$   and $$\angle6$$  are:

• Supplementary

• Complementary

• Congruent

• Not enough information to determine

Open Ended

Select a pair of angles. State if the angles are supplementary or congruent, and explain your reasoning.

Open Ended

If $$m\angle1\ =\ 65\degree$$  , state the measure of $$\angle7$$  . Explain your reasoning