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
midpoint theorem
if M is the midpoint of segment AB then AM = 1/2AB and MB = 1/2AB
angle bisector theorem
if ray OB bisects
complementary angles
2 angles whose sum is 90
supplementary angles
2 angles whose sum is 180
linear pairs
two adjacent angles whose exterior sides are opposite rays
vertical angles
the same vertex, both sides make opposite rays with each other, NOT adjacent
theorem 2-3 vertical angles are ______
congruent
