Unit 2 Quiz Terms Flashcards
Study Properties, Definitions, Postulates, and Theorems
Addition Property of Equality
If a = b, then a+c = b+c
Subtraction Property of Equality
If a = b, then a-c = b-c
Multiplication Property of Equality
If a = b, then ac = bc
Division Property of Equality
If a = b and c ≠ 0, then a÷c = b÷c
Distributive Property
If a(b+c), then a(b+c) = ab+ac
Substitution Property
If a = b, then “a” may be replaced by “b” in any expression or equation.
Reflexive Property of Equality
For any real number a, a=a. (a value will always equal itself)
Symmetric Property of Equality
If a = b, then b = a
Transitive Property of Equality
If a = b and b = c, then a = c
What are the properties of equality used for?
Justifying steps in solving an equation
What is a Two-Column Proof?
A common format used to organize a proof.
What goes on the left side of a Two-Column Proof?
The statements/steps
What goes on the right side of a Two-Column Proof?
The reasons that justify each step
What can be used as reasons?
Definitions, Postulates, Theorems, and Properties
What are the 9 properties of equality?
- Addition Property of Equality
- Subtraction Property of Equality
- Multiplication Property of Equality
- Division Property of Equality
- Distributive Property
- Substitution Property
- Reflexive Property of Equality
- Symmetric Property of Equality
- Transitive Property of Equality
Reflexive Property of Congruence
For any segment AB, AB ≅ AB (there is a line above the segment but I can’t type it on the flashcard)
Symmetric Property of Congruence
If AB ≅ CD and CD ≅ EF, then AB ≅ EF (there is a line above the segment but I can’t type it on the flashcard)
Transitive Property of Congruence
If AB ≅ CD and CD ≅ EF, then AB ≅ EF (there is a line above the segment but I can’t type it on the flashcard)
Definition of Congruence (Congruence)
Segments are congruence if and only if they have the same measure
Definition of Midpoint
The midpoint of a segment divides the segment into 2 equal/congruent parts.
Ex. If M is the midpoint of AB, then AM = MB.
Segment Addition Postulate
If A, B and C are collinear points and B is between A and C.
Ex. AB + BC = AC
Definition of Congruence (Angle)
m<A = m<B <–> <A ≅ <B
Definition of Angle Bisector
An angle bisector divides an angle into two equal parts (= or ≅)
Definition of Complementary Angles
Complementary <–> Sum is 90º
Definition of Supplementary Angles
Supplementary <–> Sum is 180º
Definition of Perpendicular
Perpendicular lines form right angles
Definition of Right Angles
A right angles = 90º
Angle Addition Postulate
m<ABD + m<DBC = m<ABC
Vertical Angles Theorem
If two angles are vertical, then they are congruent
Vertical Angles Theorem Abbreviation
VAT
Complement Theorem
If two angles form a right angle, then they are complementary. Right Angle–> Complementary.
Supplement Theorem
If two angles form a linear pair, then they are supplementary. Linear pair–> Supplementary.
Congruent Complements Theorem
If <A is complementary to <B and <C is complementary to <B, then <A ≅ <C
Congruent Supplementary Theorem
If <A is supplementary to <B and <C is supplementary to <B, then <A ≅ <C
What is the abbreviation of property of equality
Prop of =
What is the abbreviation of property of congruence
Prop of ≅
