ratio of a to b
 two quantities measured in the same units; a:b, a/b
 proportion
 an equation that equates two ratios.
 Cross Product Property
 the product of the extremes equals the product of the means
 reciprocal property
 if two ratios are equal, their reciprocals are also equal
 extremes
 the letters a and d are the extremes of a proportion a:b=c:d
 means
 the numbers b and c are the means of the proportion a:b =c:d
 similar polygons
 when there is a correspondence between two polygons such that their corresponding angles are congruent and their corresponding sides are proportional
 Side -side-side similarity theorem
 if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
 dilation
 a transformation that maps every point in a plane to the final image so that the following is true:1. if p is not the center C, then the image point p’ lies on CP. the scale factor k is a positive number such that k=CP’/CP’ and k does not equal 12. if P is the center point C, the P=P’
 special right triangles
 triangles whose measures are 45-45-90 or 30-60-90
 trigonometric ratio
 a ratio of the lengths of two sides of a right triangle
 three basic trigonometric ratios
 sine, cosine, tangent
 sin A
 side opposite angle A over hypotenuse
 Cosine
 tangent
 angle of elevation
 the angle your line of sight makes with a line drawn horizontally
 circle
 set of all points in a plane equidistant from a given point
 distance from the center to a spot on the circle
 congruent circles
 diameter
 distance across the circle, through its center
 chord
 a segment whose endpoints are points on the circle
 secant
 a line that intersects a circle in two points
 tangent
 a line that intersects the circle in exactly one point
 concentric circles
 circles with the same center
 interior of a circle
 consists of all points+ within the circle
 exterior of a circle
 all points outside of the circle
 point of tangency
 the point where the line of tangency intersects the circle to which it is tangent
 central angle
 in a plane, an angle whose vertex is the center of a circle
 minor arc
 an arc of the circle that is less than 180 degrees
 major arc
 an arc with measure greater than 180 degrees
 measure of the major arc
 the difference between 360 and the minor arc
 inscribed angle
 an angle whose vertex is the center of the circle and whose sides contain chords of the circle
 intercepted arc
 the arc that lies in the interior of an inscribed angle and has endpoints on the angle
 inscribed polygon
 all vertices lie on the circle
 circumscribed
 a circle that included an inscribed polygon
 tangent segment
 is tangent to the circle at an endpoint
 secant segment
 is secant to the circle with an endpoint on the circle
 standard equation of a circle with radius(r) and center(h,k)
 (X-H)2 + (Y-K)2=r2
 locus
 in a plane, it’s the set of all points in a plane that satisfy a given condition or a set of given conditions
 polygon interior angles theorem
 the sum of the measures of the interior angles of a convex n-gon is (n-2)x i80
 polygon exterior angles theorem
 the sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360 degrees
 corrollary to thrm 11.2
 the measure of each exterior angle of a regular n-gon is 1/n x 360
 area of an equilateral triangle
 is one fourth the square of the lengths of the side times root 3
 center of the polygon and radius of the polygon
 are the radius and center of its circumscribed circle
 apothem of the polygon
 the distance from the center of the polygon to any side
 area of a regular polygon
 half the product of apothem a x Perimeter
 central angle of a regular polygon
 an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon
 arc length
 measure arc AB over 360 x 2(pi)radius
 sector of a circle
 region bound by two radii of the circle and their intercepted arc
 probability
 number from 0 to 1 that represents the chance an event will occur
 polyhedron
 a solid bound by polygons, called faces, that enclose a single region of space
 edge of a polyhedra
 is a line segment formed by the intersection of two faces
 vertex
 point where 3 or more edges meet
 euler’s theorem
 faces +vertices=edges+2
 platonic solids
 tetrahedron, cube, octahedron, dodecahedron, icosahedron
 prism
 a polyhedra with 2 congruent faces, called bases
 lateral faces
 parallelograms formed by connecting the corresponding vertices of the bases
 right prism
 all lateral edges are perpendicular to the bases
 surface area of a right prism
 S=2B+Ph
 cylinder
 a solid with congruent circular bases that lie in parallel planes
 surface area of a right cylinder
 SA of a regular pyramid
 B+1/2 Pl
 cone
 has a circular base and a vertex that is not in the same plane as the base
 lateral surface of a cone
 consists of all segments that connect the vertex with points on the base edge
 volume of a cylinder
 Bxh=pi(r)squared x heght
 volume of a cone
 1/3 base x height
 volume of a cone
 1/3 pi(r)squared x height
 sphere
 locus of all points in SPACE that are a given distance from a point, called the center of the sphere