Postulates
What Postulate says:
If B is between A and C, then AB+BC=AC
Segment Addition Postulate (Postulate 2)
If a=b, then a+c=b+c
What is the Addition Property of Equality?
This Theorem says angle congruence is reflexive, symmetric, and transitive.
Theorem 2.2 Congruence of Angles
Pg. 127 # 5
See Board
Postulate 7
What is: If two lines intersect, then their intersections is exactly 1 point?
If a=b, then ac=bc
What is the multiplication property of equality?
This theorem says: segment congruence is reflexive, symmetric, and transitive.
What is Theorem 2.1 Congruence of Segments
pg 128 #9
168o, 12o, 12o
Postulate 3 (Protractor Postulate)
What is: With a ray OB and a point A on one side of the ray OB. The ray of the form OA can be match one to one with the real numbers.
What is the Reflexive property of equality?
For any real number a, a=a.
For any segment AB, AB=AB.
For any angles A and B, if mA=mB, mB=mA.
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
What is the congruent supplements theorem? (Theorem 2.4)
pg 128 #16
D
This postulate says: If two planes intersect, then their intersection is a line.
What is Postulate 11?
For any numbers a, b, and c; if a=b and b=c, then a=b.
What is the Transitive Property?
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
What is the Congruent Complements Theorem? (Theorem 2.5)
pg 128 #19
27o
What is : A plane contains at least three non-collinear points?
How are the substitution and transitive properties different?
Example answer: In substitution, a value is replaced. In transitive and entire expression (side of the equation/congruence) is replaced.
What theorem says Vertical angles are congruent?
Theorem 2.6 Vertical Angles Theorem
pg 129 #31
Angle FGH and Angle EGH; Definition of Angle Bisector