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.
If <AFC is congruent to <EFC, then line AE is perpendicular to line FC.
If two lines form congruent adjacent angles, the lines are perpendicular.
Memorize
(If the exterior of…)
If the exterior of two adjacent acute angles are perpendicular, then the angles are complementary.
<1 is supp. to <2
<3 is supp. to <4
<2 is congruent to <3
<1 is congruent to <4
Supplements of congruent angles (or the same angle) are congruent.
<6 is comp. to <7
<8 is comp. to <9
<7 is congruent to <8
<6 is congruent to <9
Complements of congruent angles (or the same angle) are congruent.
Through any 2 points there is exactly __ line.
Through any 2 points there is exactly one line.
A line contains at least __ points; a plane contains at least __ points not all in one line; space contains at least __ points not all in one plane.
A line contains at least 2 points; a plane contains at least 3 non-collinear points; space contains at least four non-coplanar points.
Through any __ points there is at least one plane.
Through any __ non-collinear points, there is exactly one plane.
Through any 3 points there is at least one plane.
Through any 3 non-collinear points, there is exactly one plane.
If __ points are in a plane, then the line that contains the points is in that plane.
If 2 points are in a plane, then the line that contains the points is in that plane.
If two planes intersect, then their intersection is a __.
If two planes intersect, then their intersection is a line.
If 2 lines intersect, then they intersect in exactly __ point.
If 2 lines intersect, then they intersect in exactly one point.
Through a line and a point not in the line, there is exactly __ plane.
Through a line and a point not in the line, there is exactly one plane.
If 2 lines intersect, then exactly __ plane contains the lines.
If 2 lines intersect, then exactly one plane contains the lines.
