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.
Parallel 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
Perpendicular Postulate
Theorem 3.1: If two lines intersect to form a linear pair of congruent angles, then the lines are ______
perpendicular
Theorem 3.2: If two sides of two adjacent acute angles are perpendicular, then the angles are _____
complementary
Theorem 3.3: If two lines are perpendicular, then they intersect to form _________
four right angles.
Corresponding Angles Postulate (CA)
if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Alternate Interior Angles Theorem (AIA)
if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Alternate Exterior Angles Theorem (AEA)
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other
Corresponding Angles Converse Postulate
two lines are cut by a transversal so that corresponding angles are congruent then the lines are parallel
Alternate Interior Angles Converse Theorem
if two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel
Alternate Exterior Angles Converse Theorem
if two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel
Consecutive Interior Angles Converse Theorem
if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel
Theorem 3.11: If two lines are parallel to the same line, then they are _______________________
parallel to each other
Theorem 3.12: If two lines are perpendicular to the same line, then they are ______________________
parallel to each other
Slopes of Parallel Lines
Two lines are parallel if and only if they have the same slope
Slopes of Perpendicular Lines
Two lines are perpendicular if and only if their slopes are opposite reciprocals
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.
Parallel 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
Perpendicular Postulate
Theorem 3.1: If two lines intersect to form a linear pair of congruent angles, then the lines are ______
perpendicular
Theorem 3.2: If two sides of two adjacent acute angles are perpendicular, then the angles are _____
complementary
Theorem 3.3: If two lines are perpendicular, then they intersect to form _________
four right angles.
Corresponding Angles Postulate (CA)
if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Alternate Interior Angles Theorem (AIA)
if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Alternate Exterior Angles Theorem (AEA)
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other
Corresponding Angles Converse Postulate
two lines are cut by a transversal so that corresponding angles are congruent then the lines are parallel
Alternate Interior Angles Converse Theorem
if two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel
Alternate Exterior Angles Converse Theorem
if two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel
Consecutive Interior Angles Converse Theorem
if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel
Theorem 3.11: If two lines are parallel to the same line, then they are _______________________
parallel to each other
Theorem 3.12: If two lines are perpendicular to the same line, then they are ______________________
parallel to each other
Slopes of Parallel Lines
Two lines are parallel if and only if they have the same slope
Slopes of Perpendicular Lines
Two lines are perpendicular if and only if their slopes are opposite reciprocals