coplanar lines that do not intersect.. lines that do not intersect and are not coplanar
TRANSCRIPT
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Define Parallel Lines
Coplanar lines that do not intersect.
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Define Skew Lines
Lines that do not intersect and are not coplanar.
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What angles are marked?
Corresponding Angles
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What angles are marked?
Alternate Interior Angles
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What angles are marked?
Consecutive Interior Angles
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What angles are marked?
Alternate Exterior Angles
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What is the Parallel Postulate?
If there is a line and a point not on the line,
then there is exactly one line through the point parallel to the given line.
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What is the Perpendicular Postulate?
If there is a line and a point not on the line,
then there is exactly one line through the point perpendicular to the given line.
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Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are
congruent.
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Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal,then the pairs of alternate interior angles
are congruent.
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Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal,then the pairs of alternate exterior angles
are congruent.
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Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles
are supplementary.
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Corresponding Angles Converse
If two lines are cut by a transversal so that the corresponding angles are congruent,
then the lines are parallel.
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Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interior angles are congruent,
then the lines are parallel.
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Alternate Exterior Angles Converse
If two lines are cut by a transversal so the alternate exterior angles are congruent,
then the lines are parallel.
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Consecutive Interior Angles Converse
If two lines are cut by a transversal so the consecutive interior angles are supplementary,
then the lines are parallel.
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Transitive Property of Parallel Lines
If two lines are parallel to the same line,
then they are parallel to each other.
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What is the slope equation?
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Slopes of parallel lines
In a coordinate plane, two nonvertical lines are parallel if and only if
they have the same slope.
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Slopes of perpendicular lines
In a coordinate plane, two nonvertical lines are perpendicular if and only if,
the product of their slopes is –1.
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Slope-intercept form
y = mx + b
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Standard Form
Ax + By = C
A, B, and C are integers
A > 0
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Different slopes
Line that is rising from left to rightSlope is positive
Horizontal lineSlope is zero
Vertical LineSlope is undefined
Line that is falling from left to rightSlope is negative
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If two lines intersect to form a linear pair of congruent angles,
then the lines are perpendicular.
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If two lines are perpendicular,
then they intersect to form four right angles.
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If two sides of two adjacent acute angles are perpendicular,
then the angles are complementary.
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Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines,
then it is perpendicular to the other.
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Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the same line,
then they are parallel to each other.