Addition Property of Eqaulity
if AB = 4 and BC = 2then AB + BC = 4 + 2
Subtraction Property of Equaltiy
If m<A +20 = 60then m<A = 40
Multiplication Property of Equality
If 1/2AC = ABthen AC = 2AB
Division Property of Equality
If 2m<A = 40then m<A = 20
Substitution Property of Equality
If m<A = m<1 and m<1 + m<B = 90then m<A + m<B = 90
Reflexive Property of Equality
DE = DE m<1 = m <1
Symmetric Property of Equality
If DE = AB, then AB = DE
Transitive Property of Equaltiy
If m<1 = m<2 and m<2 = m<3,then m<1 = m<3
Reflexive Property of Congruence
AB ≅ AB
Symmetric Property of Congruence
If AB ≅ DE, then DE ≅ AB
Transitive Property of Congruence
If AB ≅ CD and CD ≅ EF, then AB ≅ EF
Definition of Congruence
Two objects that have the same shape and size.
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Segment Addition Postulate
adding 2 segment pieces to equal a whole segment
Angle Addition Postulate
Suppose you break an angle into two smaller angles. This postulate says that the sum of the measures of the two angles should add up to the measure of the big angle.
Angle Addition Postulate
if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC
midpoint of a segment
The point that divides the segment into two congruent segments
midpoint of a segment
the point where the bisector intersects a segment
congruent segments
two segments are congruent if they have the same length. segment AB is congruent to segment XY if and only if distance AB = distance XY
bisector of a segment
a line, segment, ray, or plane that intersects a segment at its midpoint
Angle Addition Postulate
is B lies in the interior of angle AOC then the measure of angle AOB + the measure of angle BOC = Angle AOC.if angle AOC is a straight angle and point B is any point not on line AC, then the measure of angle AOB + the measure of angle BOC = 180 degrees
congruent angles
Use tick marks to signify, angles with the same measure
congruent angles
angles that have equal measures
adjacent angles
are a pair of angles with a common vertex and a common side, but no common interior points
angle bisector
a ray that divides an angle into two congruent, adjacent angles
Substitution Property
if a=b then either a or b may be substituted for the other in any equation ( or inequality)
Subsitution Property
If m<1 + m<2 = 180 and m<3 + m<4 = 180then m<1 + m<2 = m<3 + m<4
Midpoint Theorem
if M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB
Anlge Bisector Theorem
if ray BX is the bisector of <ABC, thenm<ABX = 1/2mXBC and m<XBC = 1/2m<ABC
Complementary Angles
two angles whose measures have a sum of 90 degrees
Supplementary Angles
two angles whose measures have a sum of 180 degrees
Vertical Angles
2 angles whose sides are opposite rays
Vertical Angle Theorem
Vertical Angles are congruent
Perpendicular Lines
Two lines that intersect to form right angles
Perpendicular Lines
Lines that intersect at 90 degree angles.
Perpendicular Lines
two lines that intersect to form a right angle. the symbol for "is perpendicular to" is ⊥
Vertical Angles are Congurent
If <1 and <2 are vertical angles, then <1 ≅ <2
Segment Addition Postulate
If XY = WZ, then XY + TU = WZ + TU
Angles supp to same angles are congurent
IF m<1 + m<2 = 180 and m<2 + m<3 = 180,then <1 ≅ <3
Midpoint Theorem
If E is the midpoint of line segment BC, then BE = 1/2BC
Angle Bisector Theorem
If ray BD bisects <ABC, then m<2 = 1/2m<ABC
Addition Property of Equality
if 6x - 7 = 29, then 6x = 36
Division Property of Equality
If 2m<1 = 100, then m<1 = 50
Conditional Statement
A logical statement that has two parts, an hypothesis and a conclusion.
Hypothesis
The "If" part of a conditional statement
Conclusion
The "then" part of a conditional statement
Property of Perpendicular Lines
If two lines are congruent, then they form congruent adjacent angles.
Property of Perpendicular Lines
If two lines form congruent adjacent angles, then the lines are perpendicular.
Property of Perpendicular Lines
If the exterior sides of 2 adjacent acute angles are perpendicular, then the angles are complementary.
Congurent Comps Theorem
If 2 angles are comps of congruent angles (or of the same angle), then the 2 angles are congruent.
Congruent Supps Theorem
If 2 angles are supps of congruent angles (or of the same angle), then the 2 angles are congruent.
Biconditional
if a conditional and its converse are both true, then the statement can be written using the words if and only if (iff)
Biconditional
a statement that contains the words "if and only if
Converse
the statement formed by switching the hypothesis and conclusion of a conditional statement
Angles comp to same angles are congruent
IF m<1 + m<2 = 90 and m<2 + m<3 = 90,then <1 ≅ <3