31 terms

# Ch. 1-2 postulates and theorems

Mcdougal Littell
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Ruler Postulate
the points on a line can be paired with all real numbers and the distance on the line is found by taking the absolute value of the difference of their coordinates.
If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.
Protractor Postulate
Given a strait angle rays can be paired with numbers from 0 to 180. the measure of an angle is the absolute value of the difference of the numbers paired with rays.
If P is in the interior of RST, then mRST=mRSP+mPST
Post. 5
A line contains at least 2 points, a plane at least 3 non collinear points, and space at least 4 non coplanar points.
Line postulate
Through any two points there exists exactly one line.
plane postulate
7, Any 3 points are contained in at least one plane, and 3 non-collinear points determine a plane.
flat plane postulate
if two points lie in a plane, then the line containing those points lies in the plane
plane intersection postulate
9, if two planes intersect, then their intersection is a line
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, if a=b and c=d, then a+c=b+d
subtraction property
If a=b and c=d, then a-c=b-d
multiplication property
If a=b, then ac=bc
division property
if a=b and c≠0, then a/c=b/c
substitution property
if a = b, then a can be substituted for b in any equation or expression
reflexive property
a=a
symmetric property
If a=b, then b=a
transitive property
If a=b and b=c, then a=c
distributive property
a(b+c)=ab+ac
line intersection theorem
2 different lines intersect in at most ONE POINT
plane determination theorem
Through a line and a point not on a line, there is exactly one plane.
midpoint theorem
if M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB
Angle Bisector theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
supplementary theorem
If two angles for a linear pair, then they are supplementary angles
verticle angle theorem
If two angles are vetical angles, then they have equal measures
2-4 theorem
perpendicular lines form congruent adjacent angles.
2-5 theorem
if 2 lines for congruent adjacent angles then they are perpendicular.
2-6
if the outside rays of two adjacent acute angles are perpendiculalr, then the angles are complementary.
supplements of congruent angles theorem
supplements of congruent angles are congruent
compliments of congruent angles theorem
compliments of congruent angles are congruent