# Postulates And Theorems

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. T3-1- IF 2 parallel planes are cut bty a 3rd plane then the lines of intersection are parallel. P10- If 2 parallel lines are cut by a transversal, hen corresponding angles are congruent. T3-2- IF 2 parallel lines are cut by a transversal then alternate interior angles are congruent.

T3-3- IF 2 parallel lines are cut by a transveral then same side interior angles are supplementary. T3-4-If a transversal is perpendicular to one of 2 parallel lines then it is perpendicular to the other one also. P11- IF 2 lines are cut by a transversal and corresponding angles are congruent then the lines are parallel. T3-5- If 2 lines are cut by a transversal and alternate interior angles are congrunt then the lines are parallel.

T3-6- If 2 lines are cut by a transversal and same side interior angles are supplementary then the lines are parallel. T3-7- In a plane 2 lines perpendicular to the same line are parallel. T3-8- Through a piont outside a line there is exactly one line parallel to the given line. T3-9- Through a point outside a line there is exactly one line perpendicular to the given line. T3-10- Two lines parallel to a 3rd line are parallel to each other. T3-11- The sum of the measures of the angles of a triangle is 180. C1- If 2 angles of one triangle are congruent to 2 angles of another triangle then the rd angless are congruent. C2- Each angle of an equianglular triangle has measure 60. C3- In a triangle there can be at most one right angle or obtuse angle.

C4- the acute of a right triangle ar complementary. T3-12- The measure of an exterior angle of a triangle equals the sum of the measure of the 2 remote interior angles. Scalene- no sides congruent. Isosceles- at least 2 sides congruent. Equilateral- all sides congruent. Acute- 3 acute angles. Obtuse- 1 obtuse angle. Right- 1 right angle. Equilangular- all angles congruent. Ways To prove to lines are parallel. 1. Show that a pair of corresponding angles are congruent. 2. Show that a pair of alternate interior angles are congruent. 3. Show that a pair of same side interior angles are supplementary. 4. In a plane show that both lines are perpendicular to a third line. 5. Show that both lines are parallel to a third line. Alternate Interior angles- are 2 nonadjacent interior angles on opposite sides of the transversal. Z Same Side Interior angles- are 2 interior angles on the same side of the transversal. U Corresponding angles- are 2 angles in corresponding postitions relative to the 2 lines.

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