Definitions, Postulates, and Theorems Chapter 1 and 2
Angle bisector (def)
A ray is an bisector it divides an into 2 ’s.
Linear Pair (def)
2 ’s are a linear pair they are adjacent ’s whose noncommon sides are opposite rays.
Midpoint (def)
A point is a midpoint it divides a segment into 2 segments.
Segment Bisector (def)
A set of points is the segment bisector intersection with the segment is the midpoint of the segment.
Perpendicular lines (def)
2 lines are perpendicular they form 4 right ’s.
Perpendicular bisector (def)
A line is a perpendicular bisector it is perpendicular to the segment and goes through the segments midpoint.
Right angles (def)
Anis right its measure is 90º.
Vertical angles (def)
2’s are vertical they are nonadjacent ’s formed by intersecting lines.
Complementary angles (def)
2 ’s.are complementary their sum is 90º.
Supplementary angles (def)
2 ’s.are supplementary their sum is 180º.
Congruence (def)
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Angle Addition Postangle + angle = angle Segment Addition Post segment + segment = segment
The sum of the parts equal the whole.
If 2’s that form a linear pair they are supplementary.
If noncommon sides of 2 adjacent ’s form a right they are complementary
If 2’s are vertical they are.
All right’s are.
If 2 's are supplementary they are right ’s.
lines form adjacent ’s.
Congruent Complements Theorem
If 2’s are complementary to the same or's they are .
Congruent Supplements Theorem
If 2’s are supplementary to the same or's they are .
Through any 2 points, there is exactly one line.
Through any 3 non-collinear points, there is exactly one plane.
A line contains at least 2 points.
A plane contains at least 3 non-collinear points.
Space contains at least 4 non-collinear, non-coplanar points.
If 2 points are lie in a plane, then the line containing those points lies in that plane.
If two lines intersect, then there intersection is exactly one point.
If 2 planes intersect, then their intersection is a line.
Logic Notes
Logic means reasoning.
A logical statement or conditional statement is called an if-then statement.
Counterexample: The figure is a quadrilateral and it’s a trapezoid.
Negation: ~p p: It is a square ~p: It is not a square
Conditional: If p, Then q. (pq) p: hypothesis q: conclusion
If it is a square, then it’s a quadrilateral.
P q
Converse: qp If q, then p. If it’s a quadrilateral, then it’s a square. (may be T or F)
Inverse: ~p~q(may be T or F)
Contrapositive: Given pq & ~q~p
pq If it’s a square, then it’s a quadrilateral.
~q~p If it’s not a quad., then it’s not a square.(T only if pq is T)
Biconditional (definition) p q (p iff q)
pq If 2 angles sum is 90 degrees, then they are complementary.
qp If 2 angles are complementary, then their sum is 90 degrees. (T both ways)
2 angles are complementary if and only if their sum is 90 degrees.
Law of Syllogism: pq, qr therefore pr (transitive property of conditionals)
Law of Detachment if pq is a true statement and p is true, then q is true.