Geometry #3 (Theorems, Postulates, Definitions) Flashcards
AM + MB = AB
AB - AM = MB
AB - MB = AM
1) Segment Addition Postulate
2) Segment Subtraction Postulate
m<AOB + m<BOC = m<AOC
m<AOC - m<AOB = m<BOC
m<AOC - m<BOC = m<AOB
1) Angle Addition Postulate
2) Angle Subtraction Postulate
a = b
b = c
a+b = b+c
Addition Property
a = b
c = d
a-c = b-d
Subtraction Property
a = b
ca = cb
Multiplication Property
a = b
a/c = b/c
Division Property
a = a
Reflexive Property
a = b , b = a
Symmetric Property
a = b
b = c
a = c
Transitive Property
a = b
c = b
a = c
Substitution Property
Def. of a Segment Bisector
A bisector of a segment is a line, segment, ray, or plane that intersects the segment at its midpoint.
Def. of a Midpoint
A midpoint divides a segment into 2
congruent segments.
Midpoint Theorem
A midpoint divides a segment in half.
Def. of an Angle Bisector
A ray that divides an angle into two congruent adjacent angles.
Angle Bisector Theorem
Forms two angles that are 1/2 the measure of the given angle.
Adjacent Angles
Two angles that share a common vertex and common side, but no common interior.
Def. of Complementary Angles
Two angles that sum of to 90* are complementary.
Def. of a Linear Pair
If two adjacent angles form a straight line, then they are supplementary.
Two angles are a linear pair if and only if they have a common side and their other sides are opposite rays.
Def. of Supplementary Angles
Two angles that sum up to 180*.
Def. of Vertical Angles
The sides of one angle are opposite to the sides of the other angle.
<1 is congruent to <2
(vertical angles)
Vertical angles are congruent.
Line a is perpendicular to line b if and only if <1 is a right angle.
Perpendicular lines form right angles.
<1 is congruent to <2
(right angles)
All right angles are congruent.
If line AE is perpendicular to line FC, then <AFC is congruent to <EFC.
If two lines are perpendicular, then they form congruent adjacent angles.