unit 3. unit 3: properties of lines and transversals
TRANSCRIPT
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Properties of Lines and Transversals
Unit 3
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Lines Cut by a TransversalUnit 3: Properties of Lines and Transversals
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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
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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
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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
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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
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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˚)
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Construction of a line parallel to a given line through a point not on the line
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Investigating Parallel Lines and Angle PairsUnit 3: Properties of Lines and Transversals
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Investigating Parallel Lines and Angle Pairs
Postulate: Statement that is assumed to be true.
Theorem: Statement that is priven to be true.
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Investigating Parallel Lines and Angle Pairs
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Investigating Parallel Lines and Angle Pairs
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Guided Practice
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Guided Practice
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Investigating Parallel LinesUnit 3: Properties of Lines and Transversals
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Investigating Parallel Lines
Definition: When the conditional statement and converse are both true. (bi-conditional statement)
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Investigating Parallel Lines
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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.
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Guided Practice