_Geometry_ Chapters 6-12 Definitions

Front 1

Indirect proof (What is it? What are the steps to make one?)

Back 1

Proof of something is true by proving that this fact cannot not be true.
Steps: 1) Assume temporarily that the conclusion is not true.
2) Reason logically until you reach a contradiction of a known fact.
3) Point out that the temporary assumption must be false, and that conclusion must then be true.

Front 2

Ratio

Back 2

the quotient of when the first number is divided by the second

Front 3

proportion

Back 3

is an equation stating that two ratios are equal

Front 4

similar polygons

Back 4

polygons that whose corresponding angles are congruent and whose corresponding sides are in proportion

Front 5

scale factor

Back 5

the ratio of the lengths of two corresponding sides of two similar polygons

Front 6

divided proportionally

Back 6

when two lengths are divided so their corresponding segments are in proportion

Front 7

geometric mean

Back 7

the square root of the product of two multiplied numbers or factors

Front 8

pythagorean triple

Back 8

a triple of integers which complete the pythagorean theorem. for example: 3, 4, and 5

Front 9

tangent

Back 9

length of opposite leg over the length of the adjacent leg

Front 10

sine

Back 10

length of opposite leg over the length of the hypotenuse

Front 11

cosine

Back 11

length of the adjacent leg over the length of the hypotenuse

Front 12

angle of depression

Back 12

the angle between the horizontal and the downward line of sight

Front 13

angle of elevation

Back 13

the angle between the horizontal and the upward line of sight

Front 14

circle

Back 14

the set of points in a plane at a given distance from a given point in that plane

Front 15

center of a circle

Back 15

the given point which is equidistant from any point on the circle

Front 16

radius

Back 16

the given distance between the circle center and any point on the circle

Front 17

chord

Back 17

a segment whose endpoints lie on a circle

Front 18

secant

Back 18

a line that contains a chord

Front 19

diameter

Back 19

a chord that contains the center of a circle

Front 20

tangent

Back 20

is a line in the plane of the circle that intersects the circle in exactly one point

Front 21

point of tangency

Back 21

the one point where a tangent and a point on a circle intersects

Front 22

sphere

Back 22

the set of all points in space at an equidistant distance from the center

Front 23

congruent circles/spheres

Back 23

circles/spheres that have congruent radii

Front 24

concentric circles

Back 24

circles that lie in the same plane and have the same center

Front 25

concentric spheres

Back 25

spheres that have the same center

Front 26

polygon inscribed in a circle

Back 26

a polygon whose endpoints all intersect points of the circle

Front 27

circumscribed circle about the polygon

Back 27

a circle which has a polygon inscribed in it

Front 28

polygon circumscribed about the circle

Back 28

a polygon that is tangent to a circle on each side

Front 29

circle inscribed in the polygon

Back 29

a polygon that is tangent to a circle on each side

Front 30

common tangent

Back 30

a line that is tangent to each of two coplanar circles

Front 31

tangent circles

Back 31

coplanar circles that are tangent to the same line at the same point

Front 32

central angle

Back 32

an angle with its vertex at the center of the circle

Front 33

minor arc

Back 33

a part of the points on a circle which measures less than 180 degrees

Front 34

major arc

Back 34

a part of the points on a circle which measures more than 180 degrees

Front 35

measure of a minor arc

Back 35

the measure of its central angle

Front 36

measure of a major arc

Back 36

360-the measure of its minor arc

Front 37

measure of a semicircle

Back 37

180 degrees

Front 38

semicircle

Back 38

half of a circle

Front 39

adjacent arcs

Back 39

arcs that have exactly one point in common

Front 40

congruent arcs

Back 40

arcs, in the same circle or in congruent circles, that have equal measures

Front 41

inscribed angle

Back 41

an angle whose vertex is on a circle and whose sides contain chords of the circle

Front 42

concurrent

Back 42

lines that intersects in one point

Front 43

locus

Back 43

a figure that is the set of all points, and only those oints, that satisfy one or more conditions

Front 44

base

Back 44

any side of a rectangle or other pallegram

Front 45

altitude

Back 45

any segment perpendicular to the line containing the base from any point on the opposite side

Front 46

height

Back 46

the lenght of the altitude

Front 47

center of a regular polygon

Back 47

the center of the circumscribed circle

Front 48

radius of a regular polygon

Back 48

the distance from the center to a vertex

Front 49

central angle of a regular polygon

Back 49

the perpendicular distance from the center of the polygon to a side

Front 50

circumference

Back 50

the length of the points making up a circle

Front 51

area of a circle

Back 51

all of the 2-dimensional space inside the circle

Front 52

sector of a circle

Back 52

a region bounded by two radii and an arc of the circle

Front 53

prism

Back 53

a solid with 2 congruent polygon bases lying in parallel planes

Front 54

altitude

Back 54

a segment joining the two base planes and perpendicular to both

Front 55

bases

Back 55

the faces of a prism that are not lateral faces

Front 56

lateral faces

Back 56

the faces of a prism that are not the bases

Front 57

lateral edges

Back 57

parallel segments that are formed by intersecting adjacent lateral faces

Front 58

right prism

Back 58

a prism which has rectangular lateral faces

Front 59

oblique prism

Back 59

a prism that is not a right prism

Front 60

prism's lateral area

Back 60

the sum of the areas of a prism's lateral faces

Front 61

total area of a solid

Back 61

the sum of the areas of all its faces

Front 62

cube

Back 62

a rectangular solid with square faces

Front 63

pyramid

Back 63

a solid with one base and polygonal lateral faces

Front 64

vertex of a pyramid

Back 64

the tip of the pyramid

Front 65

altitude of a pyramid

Back 65

the segment from the vertex perpendicular to the base

Front 66

lateral faces

Back 66

the triangular faces of a pyramid which share a common vertex

Front 67

lateral edges

Back 67

segments formed by intersecting lateral faces

Front 68

regular pyramids

Back 68

pyramids where:
1) the base is a regular polygon
2)all lateral edges are congruent
3) all lateral faces are congruent isosceles triangles
4) the altitude meets the base at its center

Front 69

slant height

Back 69

the height of a lateral face

Front 70

cyllinder

Back 70

is like a prism except that its bases are circles instead of polygons

Front 71

right sylinder

Back 71

a cyclinder in which the segment joining the centers of the circular bases is an altitude

Front 72

radius of the base of a cylinder

Back 72

is the radius of the cylinder

Front 73

cone

Back 73

is like a pyramid except that its base is a circle instead of a polygon

Front 74

similar solids

Back 74

soldids that have the same shape but not necessarily the same size

Front 75

inverse

Back 75

if not p, then not q

Front 76

contrapositive

Back 76

if not q, then not p

Front 77

venn diagram

Back 77

a diagram which represents a conditional

Front 78

logically equivalent statements

Back 78

statemes that are either both true or both false