Geo Final

Front 1

Parallel Postulate

Back 1

through a point not on a line there is exactly one line parrallel to given line

Front 2

Theroem 16: equidistant

Back 2

In a plane 2 points each equidistant from the endpoints of a line segment determine the perpendicular bisector of the line segment

Front 3

theoroem 17: corresponding angles

Back 3

Equal corresponding angles mean the lines are parallel

Front 4

theoroem 17: corollary 1 alternate angles

Back 4

equall alternate interior angles mean the line parallel

Front 5

theoroem 17: corollary 2 supplemenntary

Back 5

supplementary interior angles on the same side of a transversal mean the lines are parallel

Front 6

theoroem 17: corollary 3 perpendicular lines

Back 6

in a plane two lines perpendicular to a third line are parallel

Front 7

Theroem 18: parallel line

Back 7

in a plane two lines parallel to a third line are parallel to each other

Front 8

theorem 19: corresponding angles

Back 8

parallel lines form corresponding angles

Front 9

theorem 19: corollary 1 alternate angles

Back 9

parallel lines form equal alternate interior angles

Front 10

theorem 19: corollary 2: supplementary interior angles

Back 10

parallel lines form supplementary interior angles on the same side transversal

Front 11

theorem 19: corollar 3: perpndicular lines

Back 11

in a plane a line perpendicular to one of two parallel lines is also perpendicular to the other

Front 12

THeoroem 20: angle sum theorm

Back 12

the sum of the angles of a triangle is 180

Front 13

theroem 20 corollary 1:

Back 13

if two angles of one triangle are qual to two angls of another triangle the third triangles are equal

Front 14

theroem 20 corollary 2:

Back 14

the acute angles of a right triangle are complementary

Front 15

theroem 20 corollary 3

Back 15

each angle of an equialteral triangle is 60

Front 16

theroem 21 exterior angle

Back 16

an exterior angle of a triangle is equal to the sum of the remote interior angles.

Front 17

theroem 22: the aas theroem

Back 17

if two angles and the side oppisote one of them in one triangle are equal to the corresponding parts of another triangle, the triangles are congruent

Front 18

theorm 23: the hl theroem

Back 18

if the hypotenuse and a leg of one right triangle are euqula to the corresponding parts of another right triangle the triangles are equal

Front 19

Theorme 24: sum of angles quadrilateral

Back 19

the sum of the angles of a quadrilaterial is 360

Front 20

therome 24 corollar 1

Back 20

a quadrilater is equanigular if it is a rectangle

Front 21

therome 25: paralleogram

Back 21

the oppisote sides and angles of a parallelgra, are equal

Front 22

theoem 26: diagnols of parallelogram

Back 22

the diagnols of a paralleogram bisect each other

Front 23

theorme 27: oppisote side

Back 23

a quadrialaterial is a parra;epgram if oppisote sides are equal

Front 24

theoem 28L oppisote angles. a

Back 24

a quadrialteral is a parraellogram if oppioste angles are equal

Front 25

theome 29: opposote sides equal

Back 25

a quadrialateral is a parrallelogram if two oppisote sides are both parallel and equal

Front 26

therom 30: bisecting

Back 26

a quadrialateral is a parrallelogram if its diagnols bisect eachotherq

Front 27

therome 31 rectangles

Back 27

all rectangles are parralgram

Front 28

theomr 32: rhombus

Back 28

all rhombus are parallelograms

Front 29

theomr 33: diagnols of rectangle

Back 29

the diagnols of a rectangle are equal

Front 30

theorm 34: diagnols of rhombus

Back 30

the diagnols of a rhombus are perpendicualr

Front 31

therome 35: base angles isoscles trapezoid

Back 31

the base angles of an isolces trapezoid are equal

Front 32

theorm 36: diagnols of isocles trapezoid

Back 32

the diagmols of an isocles trapezioid are equal

Front 33

therome 37: midsegment theorm

Back 33

A MIDSEGMENT OF A TRIANGLE IS PARALL TO THIRD SIDE AND HALF AS LONG

Front 34

AREA OF RECTANGLE

Back 34

BASE TIMES HEIGHT

Front 35

AREA OF SQUARE

Back 35

SQUAR OF ITS SIDE

Front 36

THEOREM 38 area right triangle

Back 36

half the product of its legs

Front 37

theomr 39: area trianlges

Back 37

half the product of any base and altidtude

Front 38

theorem 40 area of parallegram

Back 38

base times altitude.

Front 39

theroem 41 area trapezoid

Back 39

half the product of it altitude and the sum of it bases

Front 40

theorem 42 pythagrem theorm

Back 40

a2+b2=c2

Front 41

theorem 44:side splitter theorem

Back 41

if a line parallel to one side of a triangle intersects the other two sides in different points it divdes the side in same ratio

Front 42

theroem 45: aa theorm

Back 42

if two angles of one triangle are equal to two angles of another trangle the triangles are similar

Front 43

theorm 46:cooresponding altitudes

Back 43

corresponding altidues of similar troangles have the same ratio as that of corresponding sides

Front 44

therom: sas similarity therom

Back 44

if an angle of one triangle is equal to an angle of another triangle and the sides including these angles are propartional then the triangles are similar

Front 45

the sss therorm similarity

Back 45

if the sides of one triangle are proportional to the sides of another triangle then the triangles ar similar

Front 46

theomr 47: perimerts of similar polygons

Back 46

the ratio of the perimeters of two similar polygons is equal to the ratio of the corresponding sides

Front 47

theomr 48: ratio of areas similar polygons

Back 47

the ratio of the areas of two similar polygons is equal to square the ration of corresponding sides

Front 48

theomr 49: altitude to hypotnuse of right traingle

Back 48

the altitude to hypotenuse of a right triangle forms two triangles similar to ir and eachother

Front 49

theorm 50: isocles right triangle

Back 49

in a isocles right triangle the hyptonuse is |2 times the length of one side

Front 50

theomr 51: 30 60 right triangle

Back 50

in a 30 60 right traingle the hypotenuse is twice th shorter leg and the longer leg is |3 times the shorter leg

Front 51

therom 52L slops parallel

Back 51

two non verticle lines are parallel iff htere slopes are equal`

Front 52

theorm 53 slopes` perpendicular

Back 52

two nonvertical lines are perpendiclar if the proudct of there slope sis -1

Front 53

Theom 56: line through center of circle

Back 53

if a line through the center of a circle is perpendiclar to chord it also bisects chord

Front 54

theom 57L line through center

Back 54

if a line through center of circle bisects chord that is not a diameter it is also perpendicular to the chord

Front 55

theorm 58: perpendicular bisector

Back 55

the perpendicualr bisecoor of a chord of a circle contains the center of circle

Front 56

theorm 59L tangent

Back 56

if a line is tangent to a circle it is perpenducr to the radius

Front 57

therom 61L equal chord

Back 57

in a circle equal chords have equal arcs

Front 58

therom 62 equal arca

Back 58

ina circle equal arc have equal chord

Front 59

theoem 63 inscribed angle

Back 59

an inscibed angle is equal to half intercepted arc

Front 60

theorem 64L a sectant angle vertex inside circle

Back 60

a sectant angle whose vertex is inside of circle is equal in measure to half the sum of the arcs intercepted by it and its vertical angle

Front 61

theorm 65 sectant angle whose vertex outside

Back 61

a sectant angle whose vertex is outside a circle is equal to measure to half the difference of its larger and smaller arcs.

Front 62

therem 66 tangent segment thorem

Back 62

the tangent segments to a circle from an external points are equal

Front 63

therom 67: intersecting chords throm

Back 63

if two chords insetect in a circle the product of the length of the segments of one chord is equal to to product of the lenghts of the segments of other chord

Front 64

therom 68:

Back 64

every triangle is cycle

Front 65

therom 69: quadrilarial is cyclic

Back 65

quadrial is cyclic is oppiote angle are supplementary

Front 66

theomr 74: regular polygons

Back 66

every regular polygon is cyclic

Front 67

therom 75: perimeter of regular polygpm

Back 67

2Nr

Front 68

theom 76 area of regular polygon

Back 68

mr2

Front 69

therom 77: circulmerfence

Back 69

2nr or nd

Front 70

therom 78: area cirlce

Back 70

nr2

Front 71

transversal

Back 71

is aline that goes across that intersects two or more lines in different .

Front 72

parallegram

Back 72

quadrilar who opposite sides are parallel

Front 73

SIMIALR

Back 73

TWO TRIANGLES ARE SIMILAR IF CORRESPONDING SIDES ARE PORPORTIONAL AND CORRESPONDING ANGLES ARE EQUAL

Front 74

tangent

Back 74

oppisote leg to the length of adjacent leg.

Front 75

sine

Back 75

oppisote to hypotenuse

Front 76

cosine

Back 76

adjacent to hypotenuse

Front 77

concentric:

Back 77

circle iff they lie in the same plane and have the same center

Front 78

radius

Back 78

center of the circle to any point on it. all radii of a circle are equal

Front 79

chord

Back 79

a chord of a circle is a line segment that connects two points of the circle

Front 80

diameter

Back 80

diameter of a circle is a chord that contains the center .

Front 81

central angle

Back 81

circle is an angle whose vertex is the center of the circle

Front 82

cyclic

Back 82

a polygon is cyclic iff there exists a circle that contains all vertices

Front 83

incenter

Back 83

angle bistects

Front 84

centroid

Back 84

medians meet

Front 85

circumcenter

Back 85

perpendicular bisector

Front 86

orthocentter

Back 86

altitudes of a triangle meet

Front 87

medians

Back 87

medians of a triangle is line segemtn that jooins vertext to the midpoint of the oppiote

Front 88

apothem

Back 88

regular polygon is perpeducuar line segment from its center to one of sides.