interim 2.1 - 2.4 Flashcards
conditional
if p, then q
p: hypothesis
q: conclusion
converse
if q, then p
counterexample
disproves a statement
are conditionals always written with the if clause first?
no
biconditional
p if and only if q
inverse
if not p, then not q
contrapositive
if not q, then not p
addition property of equality
if a = b and c = d then a + c = b + d
add same thing to each side
subtraction property of equality
if a = b and c = d then a - c = b - d
subtract same thing from both sides
multiplication property of equality
if a = b then ca = cb
multiply the same thing on each side
division property of equality
a = b and c does not equal 0 then a/c = b/c
divide the same thing on each side
substitution property of equality
if a = b then either a or b may be substituted for the other in any equation
reflexive property of equality
a = a
symmetric property of equality
if a = b then b = a
transitive property of equality
if a = b and b = c then a = c
two column proof
reasons and statements
segment addition postulate
if B is between A and C, then AB + BC = AC
angle addition postulate
if B lies in the interior of
linear pairs property
if two angles form a linear pair, then their sum is 180.
through any two points there is ______
exactly one line
definition of congruence
two figures are congruent if and only if they have the same measure
definition of a midpoint
a point is a midpoint if and only if it divides a segment into two congruent segments
definition of a segment bisector
a line, a ray, or a segment is a segment bisector if and only if it intersects a segment at its midpoint
definition of an angle bisector
a ray or a line is an angle bisector if and only if it divides the angle into two congruent adjacent angles
