Properties of Equality
What is the addition and subtraction property if A=B?
Addition: A+C = B+C
Subtraction: A-C = B-C
What is Reflexive Property of Congruence?
Segment AB ≅ Segment AB
It is a RAY that divides an angle into two congruent angles
What is the Symbolic form of the Segment Addition Postulate?
Segment AB + Segment BC = Segment AC
A statement that is believed to be true.
Conjecture
What is the multiplication and division property if A=B?
Multiplication: AxC = BxC
Division: A/C = B/C
What is Symmetric Property of Congruence?
If Segment AB ≅ Segment CD, then Segment CD ≅ Segment AB
What is the definition of Perpendicular?
When two lines intersect and form right angles
What is the symbolic form of the Angle Addition Postulate?
The measure of angle ABD + angle DBC = angle ABC
Symbolic form of Conditional Statement
p-> q
Apply the Distributive Property to A(B+C).
AB+AC
What is Transitive Property of Congruence?
If Segment AB ≅ Segment CD and Segment CD ≅ Segment EF then Segment AB ≅ Segment EF
What are angles called that add up to 180 degrees? What about 90 degrees
Supplementary and Complementary angles
If angle ABD = 76 and Ray AD is an angle bisector, what is the measure of angle ABC?
152 Degrees
Symbolic form of Inverse
~p -> ~q
What is the literal language for Symmetric Property?
If A = B then B = A
Create an example of the Transitive Property of Congruence
See boards
What is the distinction between a Linear Pair and Supplementary angles?
Both can be true at the same time, but Linear Pairs share a common side and are adjacent angles
Point B lies between points A and C on a line. If AB = 2x + 3, BC = x – 1, and AC = 14, what is the value of AB?
x=4
AB= 11
Symbolic form of Converse
q -> p
What property uses A=B, B=C, and A=C?
Transitive Property
What is the difference between the properties of equality and the properties of congruence?
Numbers and Shapes - Explain*
Which of the following types of statements best describe the Definition of Congruence:
"The measure of two angles are equal if and only if the angles are congruent"
A. Conditional Statement
B. Biconditional Statement
C. Postulate
D. Theorem
Ray BD lies in the interior of ∠ABC. If ∠ABD = 3x + 5, ∠DBC = 2x – 1, and ∠ABC = 64°
what is the value of DBC
x=12
DBC= 23
Symbolic form of Biconditional Statement
p harr q