Term
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Definition
| The square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs. |
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Term
| Pythagorean Thm. Converse |
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Definition
| If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is a right triangle. |
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Term
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Definition
| The area of a parallelogram is the product of any base and corresponding altitude. |
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Term
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Definition
| The area of a trapezoid is half the product of its altitude and the sum of its bases. |
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Term
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Definition
| The area of a rectangle is the product |
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Term
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Definition
| The area of a rectangle is the product of its base and altitude. |
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Term
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Definition
| The area of a square is the square of its side. |
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Term
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Definition
| If a line parallel to one side of a triangle intersects the other two sides in different points, it divides the sides in the same ratio. |
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Term
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Definition
| If a line parallel to one side of a triangle intersects the other two sides in two sides in different points, it cuts off segments proportional to the sides. |
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Term
| Altitudes of Similar Triangles |
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Definition
| Corresponding altitudes of similar triangles have the same ratio as that of the corresponding sides. |
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Term
| Perimeters of Similar Polygons |
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Definition
| The ratio of the perimeters of two similar polygons is equal to the ratio of the corresponding sides. |
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Term
| Areas of Similar Polygons |
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Definition
| The ratio of the areas of two similar polygons is equal to the square of the ratio of the corresponding sides. |
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Term
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Definition
| The cosine of an acute angle of a right triangle is the ratio of the length of the adjacent leg to the length of the hypontenuse. |
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Term
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Definition
| The sine of an acute angle of a right triangle is the ratio of the length of the opposite leg to the length of the hypotenuse. |
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Term
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Definition
| The tangent of an acute angle of a right triangle is the ratio of the length of the oppisite leg to the length of the adjacent leg. |
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Term
| Thm. 49 (The altitude to the hypotenuse of a right triangle forms...) |
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Definition
| The altitude to the hypotenuse of a right triangle forms two triangles similar to it and to each other. |
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Term
| Thm. 49 Cor. 1 (The altitude to the hypotenuse of a right triangle is the...) |
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Definition
| The altitude to the hypotenuse of a right triangle is the geometric mean between the segments into which it divides the hypotenuse. |
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Term
| Thm. 49 Cor. 2(Each leg of a right triangle...) |
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Definition
| Each leg of a right triangle is the geometric mean between the hypotenuse and its projection on the hypotenuse. |
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Term
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Definition
| In an Isoscles right triangle, the hypotenuse is root 2 times the lenght of a leg. |
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Term
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Definition
| In a 30-60 right triangle, the hypotenuse is twice the shorter leg and the longer leg is root 3 times the shorter leg. |
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Term
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Definition
| If the sides opposite angle A, angle B, and angle c of triangle ABC have lengths a, b, and c, then c squared equals a squared plus b squared minus 2ab cos C |
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Term
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Definition
| Two nonvertical lines are parallel iff their slopes are equal. |
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Term
| Slopes of Perpendicular Lines |
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Definition
| Two nonvertical lines are perpendicular iff the product of their slopes is -1. |
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Term
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Definition
| If a line through the center of a circle is perpendicular to a chord, it also bisects the chord. |
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Term
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Definition
| A secant angle whose vertex is inside a circle is equal in measure to half the sum of the arcs intercepted by it and its vertical angle. |
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Term
| Thm. 56 (Ifenter a line through a center...) |
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Definition
| If a line through the circle is perpendicular to a chord, it also bisects the chord. |
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Term
| Thm 63 cor.1 ( Inscribed angles that intercept...) |
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Definition
| Inscribed angles that intercept the same arc are equal. |
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Term
| Thm. 59 (If a line that is tangent to a circle...) |
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Definition
| If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of contact |
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Term
| Thm. 74 ( Every regular...) |
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Definition
| Every regular polygon is cyclic. |
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Term
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Definition
| If the radius of a circle is r, its circumference is 2pi r. |
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Term
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Definition
| If the radius of a circle is r, its area is pi r squared. |
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Term
| Postulate 11 (If two points...) |
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Definition
| If two points lie in a plane, the line that contains them lies in the plane. |
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Term
| Postulate 12 (If two planes...) |
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Definition
| If two planes intersect, they intersect in a line. |
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Term
| Postulate 14 (The volume of any prism...) |
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Definition
| The volume of any prism is the product of the area of its base and its altitude: V equals B.h. |
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Term
| Thm 79. (The length of a diagonal...) |
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Definition
| The length of a diagonal of a rectangular solid with dimensions l,w, and h is the square root of l squared plus w squared plus h squared. |
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Term
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Definition
| The volume of any pyramid is one-third of the product of the area of its base and its altitude: formula |
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Term
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Definition
| The volume of a cylinder is the product of the area of its base and its altitude. |
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Term
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Definition
| The volume of a cone is one-third of the product of the area of its base adn its altitude. |
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Term
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Definition
| The volume of a sphere is 4/3 pi r cubed. |
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Term
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Definition
| The surface area of a sphere is 4pi times the square of its radius. |
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Term
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Definition
| If the ratio of a pair of corresponding dimensions of two similar solids is r, then the ratio of their surface areas is r squared. |
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Term
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Definition
| If the ratio of a pair of corresponding dimensions of two similar solids is r, then the ratio of their volumes is r cubed. |
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Term
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Definition
| a perpendicular line segment from a vertex of a triangle to the line of the opposite side. |
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Term
| Altitude of a Quadrilateral |
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Definition
| A perpenidicular line segment that connects points on the lines of the parallel sides. |
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Term
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Definition
| The ratio of the number a to the number b is the number a/b. |
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Term
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Definition
| An equality between two ratios. |
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Term
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Definition
| The number b is the geometric mean between the numbers a and c iff a, b, and c are positive and a/b=b/c. |
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Term
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Definition
| Two triangles for which there is a correspondence between their vertices such that their corresponding sides are proportional and their corresponding angles are equal. |
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Term
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Definition
| A line in the plane of a circle that intersects the circle in exactly one point. |
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Term
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Definition
| Circles that lie in the same plane and have the same center. |
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Term
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Definition
| Circles that lie in the same plane and have the same center. |
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Term
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Definition
| A line segment that connects two points of a circle. |
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Term
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Definition
| A line that intersects a circle in two points. |
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Term
| Apothem of a Regular Polygon |
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Definition
| A perpendicular line segment from the center of the polygon to one of its sides. |
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Term
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Definition
| The limit of the areas of inscribed regular polygons. |
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Term
| Two planes or a line and a plane |
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Definition
| Two planes, or a line and a plane are parallel iff they do not intersect. |
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Term
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Definition
| Two lines are skew iff they are not parallel and do not intersect. |
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Term
| Line and a plane are perpendicular |
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Definition
| A line and a plane are perpendicular iff they intersect and the line is perpendicular to every line is the plane that passes through the point of intersection. |
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Term
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Definition
| A polyhedron is a solid bounded by parts of intersecting planes. |
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Term
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Definition
| suppose that a and b are two parallel planes, r is a polygonal region in one plane, and l is a line that intersects both planes but not r. The solid made up of all segments parallel to line l that connect a point of region r to a point of the other plane is a prism. |
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Term
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Definition
| A cross section of a geometric solid is the intersection of a plane and the solid. |
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Term
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Definition
| A sphere is the set of all points in space that are at a given distance from a given point. |
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