Geometry Theorems

Front 1

the distance postulate

Back 1

to every pair of different points there corresponds a unique positive number

Front 2

The Ruler Postulate

Back 2

To every point of the line corresponds exactly one real number, to every real number corresponds exactly one point on the line, and the distance between any two points is the absolute value of the difference of the corresponding numbers

Front 3

The Ruler Placement Postulate

Back 3

Given two points P and Q on a line, P is zero and the coordinate of Q is positive

Front 4

The Line Postulate

Back 4

For every two points there is exactly one line that contains both points

Front 5

Every plane contains (points)

Back 5

at least three noncollinear points

Front 6

Space contains (points)

Back 6

at least four noncollinear points

Front 7

IF two points on a line lie in a plane, the the line

Back 7

lies in the same plane.

Front 8

The Plane Postulate

Back 8

Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane.

Front 9

If two plane intersect their intersection is a

Back 9

line

Front 10

To every angle there corresponds a number between

Back 10

0-180

Front 11

Angle Addition Postulate

Back 11

Self-explanatory

Front 12

The Supplement Postulate

Back 12

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

Front 13

The SAS postulate

Back 13

SAS congruence

Front 14

ASA postulate

Back 14

ASA congruence

Front 15

SSS postulate

Back 15

SSS congruence

Front 16

the Parallel postulate

Back 16

through a given external point there is only one parallel to a given line

Front 17

The Area Postulate

Back 17

To every polygonal region there corresponds a unique positive real number

Front 18

The Congruence Postulate

Back 18

If two triangles are congruent then their triangular regions have the same area.

Front 19

The Area Addition Postulate

Back 19

If two polygonal regions intersect only in edges and vertices (or do not intersect at all) then their area is the union of the sum of their areas.

Front 20

The Unit Postulate

Back 20

The area of a square region is the square of the length of its edges

The are of a rectangle is the product of the altitude and the area of the base

Front 21

If A B and C are three different points of the same line then exactly one of them is

Back 21

in between the other two

Front 22

Given a line and a point not on the line

Back 22

there is exactly one plane containing both.

Front 23

Given two intersecting lines

Back 23

there is exactly one plane containing it.

Front 24

If two angles are complementary then they are

Back 24

acute angles

Front 25

If two angle are congruent and supplementary then each is a

Back 25

right angle

Front 26

The Supplement Theorem

Back 26

supplements of congruent angles are congruent

Front 27

The Complement Theorem

Back 27

Complements of congruent angles are congruent

Front 28

The Vertical Angle Theorem

Back 28

Vertical angles are congruent

Front 29

If two intersecting lines form one right angle

Back 29

then they form four right angles

Front 30

The Angle Bisector Theorem

Back 30

Every angle has exactly one bisector

Front 31

The Isosceles Triangle theorem

Back 31

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

Front 32

Converse Isosceles Triangle Theorem

Back 32

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

Front 33

The Perpendicular Bisector Theorem

Back 33

The perpendicular bisector of a segment in a plane is the set of all points of the plane that are equidistant from the end points of the segment

Front 34

Parts theorem

Back 34

the part is smaller than the whole

Front 35

The Exterior angle theorem

Back 35

exterior is greater than remote. In fact, exterior is the sum of the two remote.

Front 36

the SAA theorem

Back 36

SAA congruence

Front 37

Hypotenuse leg Theorem

Back 37

if the hypotenuse and one leg is congruent and it's a right triangle, they're congruent

Front 38

Longer side angle theorem

Back 38

Longer side is opp of larger side and smaller side smaller angle, if it's the same triangle.

Front 39

If two angles of a triangle are not congruent then the sides

Back 39

are not congruent

Front 40

The first minimum theorem

Back 40

the shortest segment is the perpendicular segment

Front 41

the triangle inequality

Back 41

the sum of the length of any two sides is greater than the length of the third side.

Front 42

the Hinge theorem

Back 42

If two sides of one triangle are congruent to two sides of another and the included angle of the first is larger, than the included angle of the second, then the side to the first one is longer to the other one.

Front 43

Converse Hinge theorem

Back 43

converse of hinge. but it's longer segment to angle instead of opposite.

Front 44

Triangle Inequality

Back 44

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

Front 45

If B and C are equidistant from P and Q then every point between B and C is

Back 45

equidistant from P and Q

Front 46

if a line and a plane are perpendicular then the plane contains every line

Back 46

perpendicular to the given point at its intersection with the given plane

Front 47

the perpendicular bisecting plane theorem

Back 47

the perpendicular bisecting plane of a segment is the set of all points equidistant from the end points of the segment

Front 48

second minimum theorem

Back 48

the shortest segment to a plane from an external point is the perpendicular segment

Front 49

two parallel lines

Back 49

lie in exactly one plane

Front 50

alternate interior

Back 50

congruent

Front 51

corresponding angles

Back 51

congruent

Front 52

same side interior

Back 52

supplementary

Front 53

if two lines are parallel to same line, then they are

Back 53

parallel to each other

Front 54

the sum of the measures of a triangle is

Back 54

180

Front 55

in a parallelogram

Back 55

opposite sides are congruent and consecutive angles are supplementary.

Front 56

the diagonal of a parallelogram

Back 56

bisects each other

Front 57

in a quad., the two opp sides are congruent

Back 57

it is a parallelogram

Front 58

in a quad if a pair of sides are both parallel and congruent

Back 58

its a parllelogram

Front 59

if diagonals of a quad bisect each other

Back 59

it's a parallelogram

Front 60

in a rhombus the diagonals are

Back 60

perpendicular to each other

Front 61

midsegment theorem

Back 61

midsegment is half and parallel to third side

Front 62

in a quadrilateral if one right angle then

Back 62

four right angle

Front 63

if the diagonals of a quadrilateral bisect each other and are perpendicular then the

Back 63

quad is a rhombus.

Front 64

the median to the hypotenuse of a right triangle is

Back 64

half as long as the hypotenuse

Front 65

30-60-90

Back 65

1, 2, square root of three

Front 66

if one leg of a right triangle is half as long as the hypotenuse

Back 66

the opposite angle has measure of 30

Front 67

parallel lines are always

Back 67

equidistant

Front 68

area of trapezoid is

Back 68

half the bases x altitude

Front 69

if two triangles ahve the same bases and altitudes

Back 69

they have the same area

Front 70

if two triangles ahve the same altitude h, then the ratio of their areas

Back 70

is the ratio of their bases

Front 71

the pythag thereom

Back 71

a^2 + b^2=C^2

Front 72

converse pythag theroem

Back 72

if using pythag theorem it fits, then it's a right triangle

Front 73

the isosceles right triangle theorem

Back 73

45-45-90 is 1-1-square root of 2

Front 74

the basic proportionality theorem

Back 74

if a line is parallel to one side of the triangle it creates similar triangles

Front 75

if a line intersects and makes proportional segments then it is

Back 75

parallel to third side

Front 76

AA similarity theorem

Back 76

triangles with this are similar

Front 77

SAS similarity

Back 77

triangles with this are similar

Front 78

SSS similarity

Back 78

triangles with this are similar

Front 79

given a right triangle and the altitude of the hypotenuse

Back 79

the altitude is the geometry mean of the segments into which it separates the hypotenuse

Each leg is the geometry mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg

Front 80

If two triangles are similar then the ratio of their areas is the

Back 80

square ratio of any two corresponding sides

Front 81

a line perpendicular to a radius at its outer end is

Back 81

tangent to the circle

Front 82

every tangent to a circle is perpendicular to the

Back 82

radius drawn to the point of contact

Front 83

the perpendicular from the center of a circle to a chord

Back 83

bisects the chord

Front 84

the segment from the center of a circle to the midpoint of a chord which is not a diameter

Back 84

is perpendicular to the chrod

Front 85

the perpendicular bisector of a chord

Back 85

passes through the center

Front 86

in the same circle or in congruent circle any two congruent chords

Back 86

are equidistant from the center

Front 87

the line-circle theorem

Back 87

if a line and circle are coplanar and the line intersects the interior of a circle then it intersects the circle in two and only two points

Front 88

a plane perpendicular to the radius at the outer end

Back 88

is tangent to the sphere

Front 89

the arc addition theorem

Back 89

you can add arcs

Front 90

the inscribed angle theorem

Back 90

the measure of an inscribed angle is half the measure of tis intercepted arc

Front 91

in the same circle or in congruent circles, if two arcs are congruent

Back 91

so are the corresponding chords

Front 92

The tangent-secant theorem

Back 92

given an angle with its vertex on a circle, formed by a secant ray and a tangent ra, the measure of the angle is half the measure fo the intercepted arc.

Front 93

the two-tangent

Back 93

if two tangent segments to a circle from a point of the exterior are congruent and determine congruent angles with the segment from the exterior point to the circle

Front 94

the median concurrence theorem

Back 94

medians of triangles when intercepted is two thirds the way

Front 95

if two arcs have equal radii

Back 95

then their lengths are proportional to their measuers