Vocabulary
What is a postulate(axiom)?
A rule accepted without proof
What is the subtraction property of equality?
The Subtraction Property of Equality states that when you subtract the same quantity from both sides of an equation, the two sides remain equal.
What is the segment addition postulate?
If a point lies between two endpoints of a line segment, the lengths of the two smaller segments add up to the length of the entire segment.
If AB=BC and BC=CD, then AB=CD. What property justifies this?
Transitive Property of Equality
If AB=12 and BC=7, with B between A and C, find AC and name the postulate used.
AC=19; Segment Addition Postulate
What is a theorem?
A rule that can be proven
What is the multiplication property of equality?
The Multiplication Property of Equality states that when you multiply both sides of an equation by the same quantity, the two sides remain equal.
What is the angle addition postulate?
If a point lies inside an angle, the measures of the two smaller angles add up to the measure of the original, larger angle.
If x=7, then x+3=10. What property justifies this?
Addition Property of Equality
Which is not a property of equality?
A. Reflexive Property
B. Transitive Property
C. Angle Addition Postulate
D. Substitution Property
C. Angle Addition Postulate
What does congruence mean?
Equal in value
Angles-have the same angle measure
Segments-have the same length
What is the reflexive property of real numbers?
The Reflexive Property of Equality states that any real number is equal to itself.
Ex. a=a
Fill in the blank:
Postulate 5 states, "Through any two ____, there exists exactly one line."
points
If x+5=12, then x=7. What property justifies this?
Subtraction Property of Equality
If x-7=11, what is x, and which property justifies adding 7 to both sides?
x=18; Addition Property of Equality
What is inductive reasoning?
The process of finding a pattern in specific cases and then writing a conjecture (observation) for the general case.
What is the Substitution Property?
The Substitution Property of Equality states that a quantity can be replaced by an equal quantity in an equation or expression.
Fill in the blank:
Postulate 8 states, "Through any three _______ points, there exists exactly one plane."
noncollinear
If a=b, then b=a. What property justifies this?
Symmetric Property of Equality
If a=b, what property says b=a?
Symmetric Property of Equality
What is deductive reasoning?
The process of using facts, definitions, accepted properties, and the laws of logic to form a logical argument.
What is the transitive property of equality for real numbers?
The Transitive Property of Equality states that if one quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first quantity is equal to the third quantity.
a=b,b=c, then a=c
Fill in the blank:
Postulate 11 states, "If two planes intersect, then their intersection point is a _______."
Line
If x=4 and y=x+2, then y=4+2. What property justifies this?
Substitution Property of Equality
A student says that two angles are congruent because they share a vertex. Is the student correct?
No. Sharing a vertex does not guarantee equal angle measures.