Postulates and theoroms Essay

This essay has a total of 859 words and 5 pages.

Postulates and theoroms

P1-Ruler Postulate.
P2-seg. add. postulate.
P3-Protractor postulate.
P4-angle add. postulate.
P5- A line contains at least two points; a plane contains at least 3 points not all in one
line; space contains at least 4 pints not all in one plane.

P6- Through any 2 points their is excatly 1 line.
P7-Through any 3 points there is at least one plane , and through any three noncollinear
points there is exactly one plane.

P8- If two points are in a plane the the line that contains the points is in that plane.
P9-If two intersect, then their intersection is a line.
T1-1-If tow lines intersect then they intersect in exactly one point.
T1-2-Through a line and a point not in the line there is exactly one plane.
T1-3- If 2 lines intersect then exactly one plane contains the lines.
Properties of equality
Add. Prop-if a=b and c=d then a c=b d
Subtraction Prop-if a=b and c=d then a-c=b-d
Mult. Prop- if a=b then ca=cb
Div Prop.-if a=b and c doesnt = 0 then a/c=b/c
Substitution prop- if a=b then either a or b may be substituded for the other in any equation.
Reflexive Property-a=a
Symmetric Property- if a=b then b=a
Transitive Prop.-if a=b and b=c then a=c.
Properties of Congruence
Reflexive Prop-Line DE is congruent to line DE. angle D=angle D
Symmetric Prop.- Line DE=FG then FG=DE. angle D=F then angle F=D.
Transitive Prop.- Line DE is congruent to line FG and line FG is congruent to JK then line DE is congruent to JK.
Distributive Prop.-a(b c)=ab ac
T2-1- IF M is the midpoint of line ab then am = half ab and mb = half ab line amb.
T2-2- If ray bx is the bisector of angle abc then m of angle abx=half the measure of angle
abc and measure of angle xbc =half m angle abc.

T2-3- Vert. angle are congruent.
T2-4- If 2 lines are perpendicular then they form congruent adjacent angles.
T2-5- IF 2 lines form congruent adjacent angles then the lines are perpendicular.
T2-6- If the exterior sides of two adjacent acute angles are perpendicular then the angles are complementary.
T2-7- IF 2 angles are supplements of congruent angles then the 2 angles are congruent.
T2-8- IF 2 angles are complements of congruent angles then the 2 angles are congruent.
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