Properties of Lines and Transversals

Unit 3

Lines Cut by a TransversalUnit 3: Properties of Lines and Transversals

Two Lines Cut by a Transversal

Angles 4 and 5 are on the inside of lines j and k and are on the same side of the transversal t, so they are _____________________. Name another pair:

Angles 4 and 6 are on the inside of lines j and k and are on opposite sides of the transversal t, so they are _____________________. Name another pair:

Angles 1 and 8 are on the outside of lines j and k and are on the same sides of the transversal t, so they are _____________________. Name another pair:

Same Side Interior Angles

Same Side Exterior Angles

Alternate Interior Angles

Two Lines Cut by a Transversal

Angles 1 and 7 are on the outside of lines j and k and are on opposite sides of the transversal t, so they are _____________________. Name another pair:

Angles 1 and 5 hold the same position in relation to their respective lines and the transversal (upper left or northwest corner) so they are ____________________. Name another pair:

Alternate Exterior Angles

Corresponding Angles

Two Lines Cut by a Transversal

Name all linear pairs (add up to 180˚) in the figure:

Name all vertical angles (congruent) in the figure:

Angles 1and 4, 4 and 3, 3 and 2, 1 and 2, 5 and 8, 8 and 7, 7 and 6, 5 and 6

Angles 1 and 3, 4 and 2, 8 and 6, 5 and 7

Parallel Lines Cut by a Transversal

What is special about the alternate interior angles when the two lines cut by a transversal are parallel?

What is special about the same side interior angles when the two lines cut by a transversal are parallel?

What is special about the alternate exterior angles when the two lines cut by a transversal are parallel?

They are congruent

They are supplementary (add up to 180˚)

They are congruent

Parallel Lines Cut by a TransversalWhat is true about the same side exterior

angles when the two lines cut by a transversal are parallel?

 What is true about the corresponding angles when the two lines cut by a transversal are parallel?

They are congruent

They are supplementary (add up to 180˚)

Construction of a line parallel to a given line through a point not on the line

Investigating Parallel Lines and Angle PairsUnit 3: Properties of Lines and Transversals

Investigating Parallel Lines and Angle Pairs

Postulate: Statement that is assumed to be true.

Theorem: Statement that is priven to be true.

Investigating Parallel Lines and Angle Pairs

Investigating Parallel Lines and Angle Pairs

Guided Practice

Guided Practice

Investigating Parallel LinesUnit 3: Properties of Lines and Transversals

Investigating Parallel Lines

Definition: When the conditional statement and converse are both true. (bi-conditional statement)

Investigating Parallel Lines

Euclid’s Parallel Postulate: If there is a line and a point not on the line, there exists exactly one line through the point that is parallel to the given line.

Guided Practice