Chapter 2 - Deductive Reasoning and Perpendicular Lines Flashcards
converse of if p, then q
if q, then p
biconditional of if q, then p
p if and only if q
addition property of equality
if a = b, c = d, then a + c = b + d
subtraction property of equality
if a = b, c =d, then a - c = b - d
multiplication property of equality
if a = b, then ca = cb
division property of equality
if a = b and c != 0, then a/c = b/c
substitution property of equality
if a = b then either a or b may be substituted for the other in any equation or inequality
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
what are the properties of congruence?
reflexive, symmetric, transitive
midpoint theorem
if M is the midpoint of AB, then AM = ½AB and MB = ½AB
angle bisector theorem
if BX is the bisector of angle ABC, them m ABX = ½mABC and mXBC = ½mABC
complementary angles
sum 90
supplementary angles
sum 180
if two lines are perpendicular
if two lines are perpendicular, they form congruent adjacent angles
if two lines form congruent adjacent angles
if two lines form congruent adjacent angles, the lines are perpendicular
if the exterior sides of two adjacent acute angles are perpendicular…
if the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary
if two angles are supplements or complements of congruent angles (or the same angle)
then the two angles are congruent
definition of perpendicular lines
two lines that intersect at a 90° angle
