GEOMETRY FINAL

tangent of a circle

a line in the plane of the cirlce that intersects the cirlcle in exactly one point. the point of intersection is called the point of ___

line of symmetery

a line that can be drawn through a plane figure so that the figure on one side is the reflection image of the figure on the opposite side

center of a circle

a point from which all given points in a plane are equidistant

convex polygon

a polygon for which there is no line that contains both a side of the polygon and a point in the interior of the polygon

n-gon

a polygon with n sides

regular polygon

a polyhedron in which all faces are congruent regular polygons

cube

a prism in which all the faces are squares

trapezoid

a quadralaterial that has exactly one pair of parallel sides

parallelogram

a quadrilateral in which both pairs of opposite sides are parallel. any side of a parallelogram may be called a base. for each base, a segment called an altitude is a segment perpendicualr to the base and having its endpoints on the lines containing the base and the opposite side.

rhombus

a quadrilateral with all four sides congruent

square

a quadrilateral with four right angles and four congruent sides

rectangle

a quadrilateral with four right triangles

sector

a region bounded by a central angle and the intercepted arc.

apothem

a segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon

pythagorean triple

a set of numbers a,b, and c that satisfy the equation a2 +b2=c2

circle

a set of points that consists of all points in a plane that are a given distance from a given point in the plane, called the center

reflection

a transformation that flips a figure over a line called the life of relection

rotation

a transformation that is the composite of two reflections with respect to two intersecting lines. the intersection of the two lines is called the center of ___

isosceles trapezoid

a trapezoid in which the legs are congruent. both pairs of base angles are congruent and the diagonals are congruent.

algle of elevation

an angle formed by a horizontal line and the line of sight to an object above the level of the horizontal

arc

an unbroken part of a circle

inscribed angle

angle having its vertex lie on a given circle and containing two chords of the circle.

angle of depression

any angle formed by a horizontal line and the line of sight to an object below the level of the horizontal

platonic solid

any one of the five regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron, or icosohedron

altitude of parallelograms

any perpendicular segment between the lines contaning two of the parellel sides.

base of a parallelogram

any side can be called the base

concentric circles

circles that lie in the same plane and have the same enter but have different radii.

semicirlce

either of the two parts into which a circle is seperated by a line containing a diameter of the cirlce

similar figures

figures that have the same shape but that may differ in size

secant

for a circle, a line that intersects the cirlce in exactly two points

chord

for a given circle, a segment whose endpoints are points on the circle. for a given sphere, a segment whose endpoints are on the sphere

central angle

for a given circle, an angle that intersects the circle in two points and has its vertex at the center of the circle. an angle formed by two segments drawn to consecutive vertices of a regular polygon from its center.

cosine

for an acute angle of a right triangle, the ratio of the length of the leg adjacent to the acute angle to the length of the hypotenuse

vertex

for an angle, the common endpoint of the two rays that form the angle

geometric mean

for any positive numbers a and b, the positive number x such that a/x = x/b

lateral area

for prisms, pyramids, cylinders, and cones, the area of the figure not including the bases

major arc

if <APB is a central angle of circle P, and Cis any point on the circle and the exterior of the angle, then points A and B and all points of the circle exterior to <APB form a major arc called ACB. three letters are needed to name the _____.

minor arc

if <APB is a central angle of circle P, then points A and B and all points on the circle interior to the angle form a minor arc called AB

diameter

in a circle, a chord that contains the centeer ofthe circle. in a sphere, a segment that contains the center of the sphere, and whose endpoints are on the sphere

transformation

in a plane, a mapping for which each point has exactly one image point and each image point has exactly one preimage point

diagonal

in a polygon, a segment joining nonconsecutive vertices of the polygon

face

in a polyhedrom, the flat polygonal surfaces tht intersect to form thee edges of the polyhedron

pythagorean theorem

in a right triangle, the sum of the squares of the measures of the legs equals the sum of the square of the measure of the hypotenus

locus

in geometry, a figure is a _____ if its the set of all points and only those points that satisfy a given condition

sphere

in space, the set of all points that are a given distance from a given point called the center

extremes

in the proportion a/d=c/d the numbers a and d

tangent of a sphere

is a line or plane that intersets the sphere in exactly one point

vertex of a pyrimad

is not contained in the base of the pyramid

base of a prism

the bases are the two faces formed by the congruent polygons that lie in parallel planes, all of the other faces being parallelograms

arc measure

the degree measure of a minor arc is the degree measure of its central angle. the degree measure of a major arc is 360 minus the degree measure of its central angle. the degree measure of a semicircle is 180

vertex of a polygon

the endpoints of the sides

base of a pyramid

the face that does not intersect the other faces at the vertex.the polygonal region

base of a cne

the flat, circular portion of the cone

circumference

the limit of the perimeters of the inscribed regular polygons as the number of sides increases.

arc length

the linear distance representing the arc. it is the part of the circumference proportional to the measure of the central angle when compared to the entire circle

volume

the measure of the amount of space enclosed by a three dimensional figure

area

the number of square units contained in the interior of a figure

base of a trapezoid

the parallel sides

cross products

the proportion is true only if the cross products are equal

base of isosceles triangle

the side opposite of the vertex angle

trigonometry

the study of properties of triangles and trigonometric functions and their appliccations

surface area

the sum of the areas of all faces and side surfaces of a three dimensional figure

tessellation

tile like patterns formed by repeating shapes to fill a plane without gaps or overlaps

congruent triangles

triangles that have their corresponding parts congruent

base of a cylinder

two congruent and parallel circular regions that form the ends of the cylinder.

vertex of a polyhedron

whre three or more edges intersect

angle of rotation

<ABC, is determined by the preimage A, the center of rotation B, and the rotation image C.

radius

1-a circle is a segment whose endpoints are the center of the circle and endpoints are the center of the circle and a point on the circle

slant height

1-for a regular pyramid, the height of lateral face. 2- for a right circular cone, the length of any segment joining the vertex to the edge of the circular base

tangent

1-for an acute angle of a right triangle, the ration of the length of the leg opposite the acute angle to the length of the leg adjacent to the acute angle

scale factor

1-the ratio of the lengths of two corresponding sides of two similar polygons 2-the ration of the lengths of two corresponding sides of two similar solids

ratio

a comparison of two numbers using division

translation

a composite of two reflections over two parallel lines. a ____ slides figures the same distance in the same direction

polygon

a figure in a plane that meets the following conditions. 1- it is a closed figure formed by three or morecoplanar segments called sides 2-sides that have a common endpoint are noncollinear. 3-each side intersects exactly two othersides, but only at their endpoints.

cylinder

a figure whose bases are formed by congruent circles in parallel planes.

quadrilateral

a four sided polygon