Postulate 2-1
Through any 2 points there is exactly 1 line
Postulate 2-2
Through any 3 collinear points there its exactly 1 plane
Postulate 2-3
A line contains at least 2 points
Postulate 2-4
A plane contains at least 3 points, not all on the same line
Postulate 2-5
If 2 points lie on a plane, then the entire line containing those 2 points lies in that plane
Postulate 2-6
2 lines intersect in exactly one point
Postulate 2-7
2 planes intersect in a line
Midpoint Theorem
If M is mp of (segment) AB then (segment) AM is congruent to (segment) MB
Ruler Postulate
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 zero, and B corresponds to a positive real number
Segment Addition Postulate
If A, B and C are collinear and B is between A and C, then AB + BC= AC. If AB+BC=AC then B is between A and C.
Theorem 2.2
Congruence of segments is reflexive, symmetric & transitive
Protractor Postulate
Given (ray) AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of (ray) AB, such that the measure of the angle formed is r.
Angle Addition Postulate
If R is in the interior of <PQS then the m<PQR and the m<RQS= the m<PQS
Supplement Theorem
If 2 <'s form a linear pair, then they are supplemenetary
Complement Theorem
If the noncommon sides of 2 adjacent angles form a right angle, then the angles are complementary angles.
Theorem 2.6
Angles supplementary to the same angle or to congruent angles are congruent
Theorem 2.7
Angles complementary to the same angle or to congruent angles are congruent
Theorem 2.9
Perpendicular lines intersect to form 4 right anlges
Theorem 2.10
ALL right angles are congruent
Theorem 2.11
Perpendicular lines form congruent adjacent angles.
Theorem 2.12
If 2 <'s are congruent and supplementary, then each angle is a right angle
Theorem 2.13
If 2 congruent <'s form a linear pair, then they are right angles.
Vertical Angles's Theorem (2.8)
Vertical Angles are Congruent