Postulates and theoroms

P1-R uler Postulate.

P2-seg. add. postulate.

P3-Protr actor 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

P1-R uler Postulate.

P2-seg. add. postulate.

P3-Protr actor 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

Substitutio n prop- if a=b then either a or b may be substituded for the other in any equation.

Reflexive Property-a=a

Symmet ric Property- if a=b then b=a

Transitive Prop.-if a=b and b=c then a=c.

Properties of Congruence

Reflexiv e 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.

Mult. Prop- if a=b then ca=cb

Div Prop.-if a=b and c doesnt = 0 then a/c=b/c

Substitutio n prop- if a=b then either a or b may be substituded for the other in any equation.

Reflexive Property-a=a

Symmet ric Property- if a=b then b=a

Transitive Prop.-if a=b and b=c then a=c.

Properties of Congruence

Reflexiv e 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.