17 terms

Chapter 3 Postulates, Theorems, and Formulas

STUDY
PLAY
Postulate 3.1 "Corresponding Angles Postulate" (HW Postulate 10)
If 2 parallel lines are cut by a transversal, then corresponding angles are congruent.
Theorem 3.1 "Alternate Interior Angles Theorem" (HW Theorem 3-2)
If 2 parallel lines are cut by a transversal, then alternate interior angles are congruent.
Theorem 3.2 "Consecutive Interior Angles Theorem" (HW Theorem 3-3)
If 2 parallel lines are cut by a transversal, then consecutive interior angles are supplementary.
Theorem 3.3 "Alternate Exterior Angles Theorem"
If 2 parallel lines are cut by a transversal, then alternate exterior angles are congruent.
Theorem 3.4 "Perpendicular Transversal Theorem" (HW Theorem 3-4)
If a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other one also.
Postulate 3.4 (HW Postulate 11)
If 2 lines are cut by a transversal, and corresponding angles are congruent, then the lines are parallel. (converse Corresponding Angles Postulate)
Theorem 3.7 (HW Theorem 3-5)
If 2 lines are cut by a transversal, and alternate interior angles are congruent, then the lines are parallel. (converse Alternate Interior Angles Theorem)
Theorem 3.6 (HW Theorem 3- 6)
If 2 lines are cut by a transversal and consecutive interior angles are supplementary, then the lines are parallel. (converse Consecutive Interior Angles Theorem)
Theorem 3.8 (HW Theorem 3-7)
In a plane, 2 lines perpendicular to the same line are parallel. (converse Perpendicular Transversal Theorem)
Theorem 3.5
If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel. (converse Alternate Exterior Angles Theorem)
Postulate 3.5 "Parallel Postulate" (HW Theorem 3-8)
Through a point outside a line, there is exactly one line parallel to the given line.
HW Theorem 3-10
2 lines parallel to a third line are parallel to each other.
Postulate 3.2 (HW Theorem 13-3)
2 non-vertical lines are parallel if and only if their slopes are equal.
Postulate 3.3
2 non-vertical lines are perpendicular if and only if their slopes are opposite reciprocals.
Point-Slope Form
(y-y₁)= m(x-x₁)
Standard Form
Ax+By=C
Point-Line Distance Formula
d=|ax₁+by₁+c|/√a²+b²