Geometry Postulates And Theorems

Front 1

segment addition postulate

Back 1

if b is between a and c then ab+bc=ac. if ab+bc=ac, then b is between a and c

Front 2

angle addition postulate

Back 2

if p is in the interior of angle rst, then m angle rsp +m angle pst= m angle rst

Front 3

linear pair postulate

Back 3

if two angles form a linear pair, then they are supplementary

Front 4

parallel postulate

Back 4

if there is a line and a pt not on the line then there is exactly one line through the pt parallel to the given line

Front 5

perpendicular postulate

Back 5

if there is a line and a pt not on the line, then there is exactly one line through the pt perpendicular to the given line

Front 6

corresponding angles postulate

Back 6

if two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent

Front 7

corresponding angles converse postulate

Back 7

if two lines are cut by a transversal so that corresponding angles are congruent then the lines are parallel

Front 8

slopes of parallel lines

Back 8

in a coordinate plane two nonvertical lines are parallel if and only if they have the same slope. any two vertical lines are parallel

Front 9

slopes of perpencicularlines

Back 9

in a coordinate plane two nonvertical lines are perpendicular if and only if the product of their slopes is -1 vertical and horizontal lines are perpendicular

Front 10

reflexive

Back 10

ab =ab

Front 11

symmetric

Back 11

if ab=cd then cd=ab

Front 12

transitive

Back 12

if ab=cd and cd=ef then ab=ef

Front 13

right angle congruence thm

Back 13

all right angles are congruent

Front 14

congruent supplements them

Back 14

if two angles are supplementary to the same angle or to congruent angles then they are congruent

Front 15

congruent complements thm

Back 15

if two angles are complementary to the same angle or to congruent angles then the two angles are congruent

Front 16

vertical angles thm

Back 16

vertical angles are congruent

Front 17

alternate interior angles thm

Back 17

if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Front 18

consecutive interior angles them

Back 18

if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

Front 19

alternate exterior angles thm

Back 19

if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent

Front 20

perpendicular transversal thm

Back 20

if a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other

Front 21

alternate interior angles converse

Back 21

if two lines are cut by a transversal so that alternate interior angles are congruent then the lines are parallel

Front 22

consecutive interior angles converse thm

Back 22

if two lines are cut by a transversal so that consecutive interior angles are supplementary then the lines are parallel

Front 23

alternate exterior angles converse

Back 23

if two lines are cut by a transversal so that consecutive interior angles are supplementary, tehn the lines are parallel

Front 24

triangle sum thm

Back 24

the sum of the measures of the interior angles of a triangle is 180 degrees

Front 25

exterior angle thm

Back 25

the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles

Front 26

third angles thm

Back 26

if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent

Front 27

base angles thm

Back 27

if two sides of a triangle are congruent then the angles opposite them are congruent

Front 28

converse of the base angles thm

Back 28

if two angles of a triangle are congruent then the sides opposite them are congruent

Front 29

perpendicular bisector thm

Back 29

if a point is on a perpendicular bisector of a segmetn then it is equidistant from the endpoints of the segment

Front 30

angle bisector thm

Back 30

if a pt is on the bisector of an anglethen it is equidistant from the two sides of the angl

Front 31

midsegment thm

Back 31

the segment connecting the midpts of two sides of a triangle is parallel to the third side and is half as long

Front 32

exterior angle inequality

Back 32

the measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles

Front 33

triangle inequality

Back 33

the sum of the lengths of any two sides of a triangle is greater than the length of the third side