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| two quantities measured in the same units; a:b, a/b |
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| an equation that equates two ratios. |
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| the product of the extremes equals the product of the means |
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| if two ratios are equal, their reciprocals are also equal |
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| the letters a and d are the extremes of a proportion a:b=c:d |
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| the numbers b and c are the means of the proportion a:b =c:d |
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| when there is a correspondence between two polygons such that their corresponding angles are congruent and their corresponding sides are proportional |
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| Side -side-side similarity theorem |
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| if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. |
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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 1
2. if P is the center point C, the P=P' |
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| triangles whose measures are 45-45-90 or 30-60-90 |
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| a ratio of the lengths of two sides of a right triangle |
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| three basic trigonometric ratios |
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| side opposite angle A over hypotenuse |
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| the angle your line of sight makes with a line drawn horizontally |
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| set of all points in a plane equidistant from a given point |
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| distance from the center to a spot on the circle |
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| distance across the circle, through its center |
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| a segment whose endpoints are points on the circle |
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| a line that intersects a circle in two points |
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| a line that intersects the circle in exactly one point |
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| circles with the same center |
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| consists of all points+ within the circle |
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| all points outside of the circle |
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| the point where the line of tangency intersects the circle to which it is tangent |
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| in a plane, an angle whose vertex is the center of a circle |
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| an arc of the circle that is less than 180 degrees |
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| an arc with measure greater than 180 degrees |
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| the difference between 360 and the minor arc |
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| an angle whose vertex is the center of the circle and whose sides contain chords of the circle |
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| the arc that lies in the interior of an inscribed angle and has endpoints on the angle |
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| all vertices lie on the circle |
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| a circle that included an inscribed polygon |
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| is tangent to the circle at an endpoint |
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| is secant to the circle with an endpoint on the circle |
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| standard equation of a circle with radius(r) and center(h,k) |
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| in a plane, it's the set of all points in a plane that satisfy a given condition or a set of given conditions |
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| polygon interior angles theorem |
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| the sum of the measures of the interior angles of a convex n-gon is (n-2)x i80 |
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| polygon exterior angles theorem |
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| the sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360 degrees |
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| the measure of each exterior angle of a regular n-gon is 1/n x 360 |
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| area of an equilateral triangle |
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| is one fourth the square of the lengths of the side times root 3 |
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| center of the polygon and radius of the polygon |
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| are the radius and center of its circumscribed circle |
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| the distance from the center of the polygon to any side |
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| area of a regular polygon |
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| half the product of apothem a x Perimeter |
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| central angle of a regular polygon |
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| an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon |
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| measure arc AB over 360 x 2(pi)radius |
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| region bound by two radii of the circle and their intercepted arc |
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| number from 0 to 1 that represents the chance an event will occur |
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| a solid bound by polygons, called faces, that enclose a single region of space |
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| is a line segment formed by the intersection of two faces |
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| point where 3 or more edges meet |
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| tetrahedron, cube, octahedron, dodecahedron, icosahedron |
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| a polyhedra with 2 congruent faces, called bases |
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| parallelograms formed by connecting the corresponding vertices of the bases |
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| all lateral edges are perpendicular to the bases |
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| surface area of a right prism |
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| a solid with congruent circular bases that lie in parallel planes |
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| surface area of a right cylinder |
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| 2B+Ch=2(pi)radius squared + 2 (pi)(r)h |
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| has a circular base and a vertex that is not in the same plane as the base |
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| lateral surface of a cone |
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| consists of all segments that connect the vertex with points on the base edge |
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| 1/3 pi(r)squared x height |
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| locus of all points in SPACE that are a given distance from a point, called the center of the sphere |
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| segment from center of sphere to sphere |
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| two solids with equal ratios of corresponding linear measures, such ash eights and radii, |
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