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
adjacent over hypotenuse
tangent
opposite over adjacent
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
radius
distance from the center to a spot on the circle
congruent circles
have the same radius
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
2B+Ch=2(pi)radius squared + 2 (pi)(r)h
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
radius of the sphere
segment from center of sphere to sphere
surface area of a sphere
4(pi)(r)squared
volume of a sphere
4/3 (pi)(r)^3
similar solids
two solids with equal ratios of corresponding linear measures, such ash eights and radii,