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40 Cards in this Set

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  • Back
inductive reasoning
the use of examples to arrive at conclusions
deductive reasoning
the use of the "premise-conclusion-reason" process(PCR process)
postulate
(axiom) a statement whose truth is assumed without proof
theorem
is a statement proved by deductive reasoning
reflexive property of equality
a quantity is equal to itself
symmetric property of equality
an equality may be reversed (if a = b then b = a)
transitive property of equality
if quantities are equal to the same quantity then they are equal to each other (if a = b and b = c then a = c)
partition postulate
a whole is equal to the sum of all its parts (property of betweenness)
substitution postulate
a quantity may be substituted for its equal in any expression
midpoint
is the point of a line segment that divides the segment into two congruent segments
angle bisector
a line, segment, or ray that passes through the vertex of an angle dividing the angle into two congruent angles
segment bisector
a line, segment, or ray that passes through the midpoint of a segment dividing the segment into two congruent segments
perpendicular lines
lines that intersect to form right angles
complementary angles
two angles whose sum is 90 degrees
supplementary angles
two angles whose sum is 180 degrees
altitude of a triangle
a line segment drawn from any vertex, perpendicular to and ending in the opposite side
right angle
an angle that measures exactly 90 degrees
straight angle
an angle that measures exactly 180 degrees (a line)
linear pair
two adjacent angles that together form a line
vertical angles
when two lines intersect the angles that lie opposite of each other
congruent
equal in measure
isosceles triangle
a triangle with two congruent sides
collinear points
points that lie on the same line
addition postulate
if equal quantities are added to equal quantities, the sums are equal
subtraction postulate
if equal quantities are subtracted from equal quantities, the differences are equal
multiplication postulate
if equal quantities are multiplied by equal quantities, the products are equal (doubles of equal quantities are equal)
division postulate
if equal quantities are divided by equal quantities, the quotients are equal (halves of equal quantities are equal)
powers postulate
the squares of equal quantities are equal
roots postulate
positive square roots of equal quantities are equal
adjacent angles
share a common vertex or side, but have no common interior points
scalene triangle
no congruent sides
acute angle
less than 90 degrees
segment
line with two endpoints
ray
continual line with one endpoint
angle
intersection of two rays
obtuse
greater than 90 degrees and less than 180 degrees
opposite rays
rays that mirror each other
<-A---B---C-> : BA and BC
premise
the "if" part of a conditional statement. it is a statement whose truth has been established, known to be true.
conclusion
the "then" part of a conditional statment. it is a statement whose truth is the result of the premise.
reason
the justification for the conclusion (definitions, properties, theorems)