Geometry Postulates And Theorems

Front 1

ruler postulate

Back 1

the points on a line can be matched ont to one with the real nimbers. the real numbers that corresponds to a pt si the coordinate of the pt. the distance between pts a and b written as ab is the absolute value of the difference between the coordinates of a and b

Front 2

segment addition postulate

Back 2

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

Front 3

protractor postulate

Back 3

consider a pt a on one side of ob. the rays of the form oa can be matched one to one with the real numbers from o to 189. the measure of angle aob is equal to the absolute value of the difference between the real numbers for oa and ob

Front 4

angle addition postulate

Back 4

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

Front 5

dslfdj

Back 5

no answer through any two pts there exists exactly one line

Front 6

sdlfj

Back 6

no answer if two lines intersect then their intersection is exactly one pt

Front 7

asdf

Back 7

no answer through any three noncollinear pts there exists exactly one plane

Front 8

asddldjfdkfj

Back 8

no answer a plane contains at least three noncollinear pts

Front 9

asdf

Back 9

no answer if two pts lie in a plane then the line containing them lies in the plane

Front 10

adfdfsafsdfs

Back 10

no answer if two planes intersect then their intersection is a line

Front 11

linear pair postulate

Back 11

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

Front 12

parallel postulate

Back 12

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 13

perpendicular postulate

Back 13

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 14

corresponding angles postulate

Back 14

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

Front 15

corresponding angles converse postulate

Back 15

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

Front 16

slopes of parallel lines

Back 16

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 17

slopes of perpencicularlines

Back 17

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 18

reflexive

Back 18

ab =ab

Front 19

symmetric

Back 19

if ab=cd then cd=ab

Front 20

transitive

Back 20

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

Front 21

right angle congruence thm

Back 21

all right angles are congruent

Front 22

congruent supplements them

Back 22

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

Front 23

congruent complements thm

Back 23

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

Front 24

vertical angles thm

Back 24

vertical angles are congruent

Front 25

askdjf

Back 25

no answer if two lines intersect to form a linear pair of congruent angles then the lines are perpendicular

Front 26

asdj

Back 26

no answer if two sides of two adjacent acute angles are perpendicular then the angles are complementary

Front 27

sdjf

Back 27

no answer if two lines are perpendicular then they intersect to form four righ angles

Front 28

alternate interior angles thm

Back 28

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

Front 29

consecutive interior angles them

Back 29

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

Front 30

alternate exterior angles thm

Back 30

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

Front 31

perpendicular transversal thm

Back 31

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

Front 32

alternate interior angles converse

Back 32

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

Front 33

consecutive interior angles converse thm

Back 33

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

Front 34

alternate exterior angles converse

Back 34

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

Front 35

akj

Back 35

no answer if two lines are parallel to the same line then they are parallel to each other

Front 36

ad

Back 36

no answer in a plane if two lines are perpendicular to the same line then they are parallel to each other

Front 37

triangle sum thm

Back 37

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

Front 38

corollary to the triangle sum thm

Back 38

the acute angles of a right triangle are complementary

Front 39

exterior angle thm

Back 39

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

Front 40

third angles thm

Back 40

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

Front 41

base angles thm

Back 41

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

Front 42

corollary to the base angles thm

Back 42

if a triangle is equilateral then it is equiangular

Front 43

converse of the base angles thm

Back 43

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

Front 44

corollary to the converse of the base angles thm

Back 44

if a triangle is equiangular, then it is equilareral

Front 45

perpendicular bisector thm

Back 45

if a pt is on a perpendicular bisector of a segmetn then it is equidistant rom the endpts of the segment

Front 46

converse of the perpendicular bisector them

Back 46

if a pt is equidistant from the endpts of a ssgment then it is on the perpendicular bisector of the segment

Front 47

angle bisector thm

Back 47

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

Front 48

converse of the angle bisector them

Back 48

if a pt is in the interior of an angle and is equidistant from the sides of the angle then it lies on the bisector of the angle

Front 49

midsegment thm

Back 49

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

Front 50

sljf

Back 50

no answer if one side of a triangle is longer than another side then the angle opposite the longer sid is larger than the angle opposite the shorter side

Front 51

sd

Back 51

no answer if one angle of a triangle is larger than another angle then the side opposite the larger angle is longer than the side opposite the smaller angle

Front 52

exterior angle inequality

Back 52

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

Front 53

triangle inequality

Back 53

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

Front 54

hinge thm

Back 54

if two sides of one triangle are congruent to two sides of another triangle and the included angle of the first is larger than the included angle of the second then the third side of the first is longer than the third side of the second

Front 55

converse of the hinge thm

Back 55

if two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longer than the third side of the second then the included angle of the first is larger than the included angle of the second

Front 56

interior angles of a quadrilateral

Back 56

the sum of the measures of the interior angles of the quadrilateal is 360 degrees

Front 57

ddks

Back 57

no answer if a quadrilateral is a parallelogram then its opposite sides are congruent

Front 58

sldj

Back 58

no answer if a quadrilateral is a parallelogram then its consecutive angles are supplementary

Front 59

sldj

Back 59

no answer if a quadrilateral is a parallelogram then its opposite angles are congruent

Front 60

lsjfjf

Back 60

no answer if a quadrilateral is a parallelogram then its diagonals bisect each other

Front 61

skd

Back 61

no answer if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram

Front 62

alsdj

Back 62

no answer if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram

Front 63

sdfjdjdj

Back 63

no answer if an angle of a quadrilateral is supplementary to both of its consecutive angles then the quadrilateral is a parallelogram

Front 64

askd

Back 64

no answer if the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram

Front 65

skdjf

Back 65

no answer if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram

Front 66

rhombus corollary

Back 66

a quadrilateral is a rhombys if and only if it has four congruent sides

Front 67

rectangle corollary

Back 67

a quadrilateral is a rectangle if and only if it is has four right angles

Front 68

square corollary

Back 68

a quadrilateral is a square if and only if it is a rhombus and a rectangle

Front 69

lksdj

Back 69

no answer a parallelogram is a rhombus if and only if its diagonals are perpendicular

Front 70

slkd

Back 70

no answer a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles

Front 71

akd

Back 71

no answer a parlalleogram is a rectangle if and only if its diagonals are congruent