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Through any two points,
there is exactly one line.
Through any three noncollinear points,
there is exactly one plane.
A line contains at least
three noncollinear points.
A plane contains at least
If two points lie in a plane,
then the entire line containing those points lies in that plane.
If two lines intersect,
then their intersection is exactly one point.
If two planes intersect,
then their intersection is a line.
if M is the midpoint of AB, then AM is congruent to MB
The points on any line or line segment can be put into one-to-one correspondence with real numbers.
Segment Addition Postulate
If A, B, and C are collinear, then point B is between A and C if and only if AB + BC = AC.
Reflexive Property of Congruence
Line AB is congruent to line AB.
Symmetric Property of Congruence
If line AB is congruent to line CD, then line CD is congruent to line AB.
transitive property of congruence
If line AB is congruent to line CD and line CD is congruent to line EF, then line AB is congruent to line EF.
Given any angle, the measure can be put into one-to-one correspondence with real numbers between 0 and 180.
Angle Addition Postulate
D is in the interior of angle ABC and only if m<ABD + m<DBC = m<ABC.
If two angles form a linear pair, then they are supplementary angles.
If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.
Angles supplementary to the same angle
or to congruent angles are congruent.
then they are congruent.
If two angles are vertical angles,
four right angles.
Perpendicular lines intersect to form
All right angles are
Perpendicular lines form
congruent adjacent angles.
If two angles are congruent and supplementary,
then each angle is a right angle.
then they are right angles.
If two angles form a linear pair,
area of triangle CAB is 30
(Postulate) If two figures are congruent, then they have to same area.
Area Addition Postulate
(Postulate) The area of a region is the sum of the areas of its non-overlapping parts.