Geometry, Teacher\'s Edition

TABLE2.3:(continued)

Type of Angle Pair Relationship

TABLE2.3:

Type of Angle Pair Relationship

Do Not Require Parallel Lines Linear Pairs Supplementary

Vertical Angles Congruent

Parallel Lines Required Corresponding Angles Congruent

Alternate Interior Angles Congruent

Alternate Exterior Angles Congruent

Consecutive Interior Angles Supplementary

Consecutive Exterior Angles Supplementary

Patty Paper Activity –When two lines are intersected by a transversal eight angles are formed in two sets of four.
When the lines are parallel, the two sets of four angles are exactly the same. To help students see this relationship,
have them darken a set of parallel lines on their binder paper a few inches apart and draw a transversal through the
parallel lines. Now they should trace one set of four angles on some thin paper (tracing paper or patty paper). When
they slide the set of four angles along the transversal they will coincide with the other set of four angles. Have
them try the same thing with a set of lines that are not parallel. This will help students find missing angle measures
quickly and remember when they can transfer numbers down the transversal. It does not help them learn the names
of the different pairs of angles which in important for communicating with others about mathematical concepts and
for writing proofs.

Additional Exercises:

1. One angle of a linear pair has a measure twice as large as the other angle. What are the two angle measures?

Answer:

x+ 2 x= 180 The angles measure 60 degrees and 120 degrees

x= 60

Proving Lines Parallel

When to Use the Converse –It takes some experience before most students truly understand the difference between
a statement and its converse. They will be able to write and recognize the converse of a statement, but then will have
a hard time deciding which one applies in a specific situation. Tell them when you know the lines are parallel and
are looking for angles, you are using the original statements; when you are trying to decide if the lines are parallel
or not, you are using the converse.

Additional Exercise:

1. Prove the Converse of the Alternate Exterior Angle Theorem.

Answer: Refer to the image used to prove the Converse of the Alternate Interior Angle Theorem in the text.

TABLE2.4:

Statement Reason

(^6) ABC∼= (^6) HF E Given
2.3. Parallel and Perpendicular Lines