Chapter 3 Postulates/Theorems

Question 1

Parallel Postulate

Answer 1

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

Question 2

Perpendicular Postulate

Answer 2

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

Question 3

Corresponding Angles Theorem

Answer 3

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

Question 4

Alternate Interior Angles Theorem

Answer 4

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Question 5

Alternate Exterior Angles Theorem

Answer 5

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent

Question 6

Consecutive Interior Angles Theorem

Answer 6

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

Question 7

Corresponding Angles Converse

Answer 7

If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel

Question 8

Alternate Interior Angles Converse

Answer 8

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel

Question 9

Alternate Exterior Angles Converse

Answer 9

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel

Question 10

Consecutive Interior Angles Converse

Answer 10

If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel

Question 11

Linear Pair Perpendicular Theorem

Answer 11

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

Question 12

Perpendicular Transversal Theorem

Answer 12

In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line

Question 13

Lines Perpendicular to a Transversal Theorem

Answer 13

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

Question 14

Slopes of Parallel Lines

Answer 14

In a coordinate plane, if two nonvertical lines are parallel if and only if they have the same slope

Question 15

Slope of Perpendicular Lines

Answer 15

In a coordinate plane, two nonvertical lines are perpendicular if and only if the products of their slopes is -1