PostulatesPostulates

1- 211- 21

Ruler postulate 1Ruler postulate 1

Points on a line that can be matched to a Points on a line that can be matched to a number linenumber line

-4 -3 -2 -1 0 1 2 3 4

Segment addition Postulate 2Segment addition Postulate 2

Adding segments togetherAdding segments together

A B C

AB+BC=AC

Protractor Postulate 3Protractor Postulate 3

Angle measured by a protractorAngle measured by a protractor

Interior angle

Angle Addition Postulate 4Angle Addition Postulate 4

m < RSP + m < PST=

M<RST

Postulate 5Postulate 5

Through any two points there exists only Through any two points there exists only one lineone line

A B

Postulate 6Postulate 6

A line contains exactly two pointsA line contains exactly two points

A B

Postulate 7Postulate 7

If two lines intersect, then their intersection If two lines intersect, then their intersection is exactly one pointis exactly one point

M

Postulate 8Postulate 8

Through any non collinear points there Through any non collinear points there exists exactly one planeexists exactly one plane

W

A B

C

Non-collinear- Not in a line

Postulate 9Postulate 9

A plane contains at least 3 non collinear A plane contains at least 3 non collinear pointspoints

A B

C D

Postulate 10Postulate 10

If two points lie on a plane, then the line If two points lie on a plane, then the line containing them lies in a planecontaining them lies in a plane

A

B

Postulate 11Postulate 11

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

Linear Pair Postulate 12Linear Pair Postulate 12

If two angles form a linear pair, then they If two angles form a linear pair, then they are supplementary.are supplementary.

1 2

M < 1 + m < 2 = 180

Parallel Postulate 13Parallel Postulate 13

If there is a line and a point not on the line, If there is a line and a point not on the line, then there is exactly one line through that then there is exactly one line through that point parallel to the given line.point parallel to the given line.

P

L

There is exactly one line through point P parallel to line L

Perpendicular Postulate 14Perpendicular Postulate 14

If there is a line and a point not on a line, If there is a line and a point not on a line, then there is exactly one line through the then there is exactly one line through the point perpendicular to the given line.point perpendicular to the given line.

P

L

There is exactly one line through P perpendicular to line L

Corresponding Angles Postulate 15Corresponding Angles Postulate 15

If two parallel lines are cut by a transversal, then the pairs of If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent, then the lines are parallel.corresponding angles are congruent, then the lines are parallel.

1 23 4

5 67 8

<1 congruent to <5

<2 congruent to <6

<3 congruent to <7

<4 congruent to <8

m

n

Corresponding Angles Converse 16Corresponding Angles Converse 16

If two lines are cut by a transversal so the If two lines are cut by a transversal so the corresponding angles are congruent, then corresponding angles are congruent, then the lines are parallelthe lines are parallel

1 23 4

5 67 8

m

n

<1 is congruent to <5

<2 is congruent to <6

<3 is congruent to <7

<4 is congruent to <8

Slope of parallel lines 17Slope of parallel lines 17

In a coordinate plane, two non vertical In a coordinate plane, two non vertical lines are parallel IFF they have the same lines are parallel IFF they have the same slope. Any two vertical lines are parallel.slope. Any two vertical lines are parallel.

Lines m and n have the same slope and are parallel

Slope of a perpendicular line 18Slope of a perpendicular line 18

In a coordinate plane, two non vertical lines are In a coordinate plane, two non vertical lines are perpendicular IFF the product of their perpendicular IFF the product of their slopes is -1slopes is -1. . Vertical and horizontal lines are perpendicularVertical and horizontal lines are perpendicular

Line m Line nLine m= - 2

Line n= 1/2

Side-Side-Side Congruence Side-Side-Side Congruence Postulate (SSS) 19Postulate (SSS) 19

If three sides of one triangle are congruent If three sides of one triangle are congruent to three sides of a second triangle, then to three sides of a second triangle, then the two triangles are congruent.the two triangles are congruent.

EX:1 Ex 2EX:1 Ex 2Q

P S W

X

Y A

B D

C

Side Angle Side Congruence Side Angle Side Congruence Postulate (SAS) 20Postulate (SAS) 20

If two sides and the INCLUDED angle of one triangle are the If two sides and the INCLUDED angle of one triangle are the congruent to two sides and the INCLUDED angle of a second congruent to two sides and the INCLUDED angle of a second triangle, then the two triangles are congruent.triangle, then the two triangles are congruent.

A

B

C

D

E

P S W Y

X

Ex:1 Ex:2Q

Angle Side Angle Congruence Angle Side Angle Congruence Postulate (ASA) 21Postulate (ASA) 21

If 2 angles and the INCLUDED side of 1 If 2 angles and the INCLUDED side of 1 triangle are congruent to 2 angles and the triangle are congruent to 2 angles and the INCLUDED side of a second triangle, then INCLUDED side of a second triangle, then the 2 triangles are congruent.the 2 triangles are congruent.