Chapters 1 & 2 Postulates, Theorems, and Formulas
Postulate 2.8 "Ruler Postulate" (HW Postulate 1)
The points on any line or line segment can be paired with real numbers so that given any 2 points, A and B on a line, A corresponds to 0 and B corresponds to a positive real number.
Postulate 2.9 "Segment Addition Postulate" (HW Postulate 2)
If A, B, and C are collinear, and B is between A and C, then AB+BC=AC. or If AB+BC=AC, then B is between A and C.
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Postulate 2.10 "Protractor Postulate" (HW Postulate 3)
Given line AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of line AB, such that the measure of the angle formed is r.
Postulate 2.11 "Angle Addition Postulate"
If B lies in the interior of <AOC, then m<AOB + m<BOC = m<AOC. If <AOC is a straight angle, and B is any point not on ray AC, then m<AOC + m<BOC = 180.
HW Postulate 5
A line contains at least 2 points; a plane contains at least 3 points not all in one line; space contains at least 4 points not all in one plane.
HW Postulate 6
Through any 2 points there is exactly one line.
HW Postulate 7
Through any 3 points, there is at least one plane, and though any 3 noncollinear points there is exactly one plane.
HW Postulate 8
If 2 points are in a plane, then the line that contains the points is in that plane.
HW Postulate 9
If 2 planes intersect, then their intersection is a line.
HW Theorem 1-1
If two lines intersect, then they intersect in exactly one point.
HW Theorem 1-2
Through a line and a point not in the line, there is exactly one plane.
HW Theorem 1-3
If 2 lines intersect, then exactly one plane contains the lines.
HW Theorem 2-1 "Midpoint Theorem"
If M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB.
HW Theorem 2-2 "Angle Bisector Theorem"
If ray BX is the bisector of <ABC, then m<ABX=1/2M<ABC and m<XBC=1/2m<ABC.
HW Theorem 2-3 "Vertical Angles Theorem"
Vertical angles are congruent.
HW Theorem 2-4
If 2 lines are perpendicular, then they form congruent adjacent angles.
HW Theorem 2-5
If 2 lines form congruent adjacent angles, then the lines are perpendicular.
HW Theorem 2-6
If the exterior sides of 2 adjacent acute angles are perpendicular, then the angles are complementary.
Theorem 2.6 (HW Theorem 2-7)
Angles supplementary to the same angle or to congruent angles are congruent.
Abbr. <'s suppl. to same < or congruent <'s are congruent
Theorem 2.7 (HW Theorem 2-8)
Angles complementary to the same angle or to congruent angles are congruent.
Abbr. <'s compl. to same < or congruent <'s are congruent