Postulates 1- 21

Ruler postulate 1 Points on a line that can be matched to a number line -4 -3 -2 -1 1 2 3 4

Segment addition Postulate 2 Adding segments together A B C AB+BC=AC

Protractor Postulate 3 Angle measured by a protractor Interior angle

Angle Addition Postulate 4 m < RSP + m < PST= M<RST

Postulate 5 Through any two points there exists only one line A B

Postulate 6 A line contains exactly two points A B

Postulate 7 If two lines intersect, then their intersection is exactly one point M

Postulate 8 Through any non collinear points there exists exactly one plane Non-collinear- Not in a line A B C W

Postulate 9 A plane contains at least 3 non collinear points A B C D

Postulate 10 If two points lie on a plane, then the line containing them lies in a plane A B

Postulate 11 If 2 planes intersect, then their intersection is a line.

Linear Pair Postulate 12 If two angles form a linear pair, then they are supplementary. M < 1 + m < 2 = 180 1 2

Parallel Postulate 13 If there is a line and a point not on the line, then there is exactly one line through that point parallel to the given line. There is exactly one line through point P parallel to line L P L

Perpendicular Postulate 14 If there is a line and a point not on a line, then there is exactly one line through the point perpendicular to the given line. There is exactly one line through P perpendicular to line L P L

Corresponding Angles Postulate 15 If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent, then the lines are parallel. <1 congruent to <5 <2 congruent to <6 <3 congruent to <7 <4 congruent to <8 1 2 m 3 4 5 6 n 7 8

Corresponding Angles Converse 16 If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel <1 is congruent to <5 <2 is congruent to <6 <3 is congruent to <7 <4 is congruent to <8 m 1 2 3 4 5 6 n 7 8

Slope of parallel lines 17 In a coordinate plane, two non vertical lines are parallel IFF they have the same slope. Any two vertical lines are parallel. Lines m and n have the same slope and are parallel

Slope of a perpendicular line 18 In a coordinate plane, two non vertical lines are perpendicular IFF the product of their slopes is -1. Vertical and horizontal lines are perpendicular Line m Line n Line m= - 2 Line n= 1/2

Side-Side-Side Congruence Postulate (SSS) 19 If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. EX:1 Ex 2 Q B X D P S W Y A C

Side Angle Side Congruence Postulate (SAS) 20 If two sides and the INCLUDED angle of one triangle are the congruent to two sides and the INCLUDED angle of a second triangle, then the two triangles are congruent. Ex:1 Ex:2 Q X B D C A E P S W Y

Angle Side Angle Congruence Postulate (ASA) 21 If 2 angles and the INCLUDED side of 1 triangle are congruent to 2 angles and the INCLUDED side of a second triangle, then the 2 triangles are congruent.