Geometry 3.1Geometry 3.1

Big Idea: Identify Big Idea: Identify pairs of lines and pairs of lines and

anglesangles

VocabularyVocabularyParallel Lines:Parallel Lines:

Two lines that do not intersect Two lines that do not intersect and are coplanar.and are coplanar.

Skew Lines:Skew Lines:

Two lines that do not intersect Two lines that do not intersect and are and are not not coplanar.coplanar.

Parallel Planes:Parallel Planes:

Two planes that do not Two planes that do not intersect.intersect.

Ex: plane RSTU || plane WXYZ Ex: plane RSTU || plane WXYZ

Note: a small triangle (like an arrow, Note: a small triangle (like an arrow, pointed in one direction of a line) is pointed in one direction of a line) is used to indicate that lines are used to indicate that lines are parallel (our book uses red color to parallel (our book uses red color to denote this) – the arrow is denote this) – the arrow is onon each each line, not at the endline, not at the end

PostulatesPostulatesPostulate 13:Parallel PostulatePostulate 13:Parallel Postulate

If there is a line and a point not on If there is a line and a point not on the line, then there is exactly one the line, then there is exactly one line through the point line through the point ║ to the ║ to the given line.given line.

PP mm

Postulate 14:Perpendicular LinesPostulate 14:Perpendicular Lines

If there is a line and a point not If there is a line and a point not on the line, then there is exactly on the line, then there is exactly one line through the point one line through the point ┴ to ┴ to the given line. the given line.

PP mm

More Vocabulary

Transversal: Transversal:

A line that intersects 2 or more A line that intersects 2 or more coplanar lines at different points.coplanar lines at different points.

Corresponding AnglesCorresponding Angles: : on on same same side of transversalside of transversal with with same same relationshiprelationship (on top or on bottom) (on top or on bottom) to other 2 lines to other 2 lines (2 & 6), others?(2 & 6), others?

Alternate Interior AnglesAlternate Interior Angles::

Angles that lie Angles that lie betweenbetween the 2 lines on opposite the 2 lines on opposite sides of the transversal sides of the transversal (3 & 5), others? (3 & 5), others?

Alternate Exterior AnglesAlternate Exterior Angles::

Angles that lie Angles that lie outsideoutside the 2 lines on the 2 lines on oppositeopposite sides of the transversal. sides of the transversal.

(2 & 8), others?(2 & 8), others?

Consecutive Interior Angles:Consecutive Interior Angles:

Angles that lie Angles that lie betweenbetween the 2 lines on the the 2 lines on the same sidesame side of the transversal. of the transversal.(4 & 5 ),others?(4 & 5 ),others?

Example: Identify all pairs of angles of the given type. • Corresponding

• Alternate Interior

• Alternate Exterior

• Consecutive interior

• Vertical

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