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Chapter 1 Vocabulary
Transcript of Chapter 1 Vocabulary
that are not formally explained by
means of more basic words and
concepts. The basic undefined terms
of geometry are point, line and plane. Undefined Term A basic undefined term of geometry. A point is a location. In a figure, points are represented by a dot. Points are named by capital letters Point A basic undefined term of geometry. A line is made up of points and has no thickness or width. In a figure, a line is shown with an arrowhead at each end. Lines are usually named by lowercase script letters or by writing capital letters for two points on the line, with a double arrow over the pair of letters Line A basic undefined term of geometry. A plane is a flat surface made up of points that has no depth and extends indefinitely in all directions. In a figure, a plane is often represented by a shaded, slanted four-sided figure. Planes are usually named by a capital script letter or by three noncollinear points on the plane. Plane Collinear Points that lie in the same place. Coplanar Line Segment Betweenness of points Between Congruent segments Construction A Q A A P Q Points that lie on the same line. F A measurable part of a line that consists of two points, called endpoints, and all of the points between them. For any two points A and B on a line, there is another point C between A and B if and only if A, B and C are collinear and AC+CB=AB. A C B For any two points A and B on a line, there is another point C between A and B if and only if A,B and C are collinear and AC+CB=AB A C B Segments that have the same measurements. A method of creating geometric figures without the benefit of measuring tools. Generally, only a pencil, straightedge, and compass are used. Midpoint Ray Segment Bisector A ray is a line. It has one endpoint and extends indefinitely in one direction. Any segment, line, or plane that intersects a segment at its midpoint. The point half way between the endpoints of a segment. Angle The intersection of two noncollinear rays at a common endpoint. The rays are called sides and the common endpoint is called the vertex. Interior A point is in the interior of an angle if it does not lie on the angle itself and it lies on a segment with endpoints that are on the side of the angle. Exterior Degree Right Angle Acute Angle Obtuse Angle Angle Bisector Adjacent Angle Linear Pair Vertical Angles Complementary Angles A point is in the exterior of an angle if it is neither on the angle nor in the interior of the angle. A unit of measure used in measuring angles and arcs. An arc of a circle with a measure of 1 degree is 1/360 of the entire circle. An angle with a degree measure of 90 An angle with a degree measure less than 90. An angle with degree measure greater than 90 and less than 180 A ray that divides an angle into two congruent angles. Two angles that lie in the same plane, have a common vertex and a common side but no interior points A pair of adjacent angles with noncommon sides that are opposite rays. Two nonadjacent angles formed by two intersecting lines. Two angles with measures that have a sum of 90. Angle 1 Angle 2 Supplementary Angles Two angles with measures that have a sum of 180. Perpendicular Lines, segments or rays that form right angles are perpendicular Polygon A closed figure formed by a finite number of coplanar segments (sides) such that
the sides that have a common endpoint are noncollinear, and
each side intersects exactly two other sides, but only at there endpoints. N-Gon A polygon with n sides. EXAMPLE A polygon with 15 sides is a 15-gon. Vertex of a polygon Convex Polygon Equilateral Polygon Equiangular Polygon Regular Polygon Perimeter Circumference Area The vertex of each angle of a polygon. Vertex Concave Polygon A polygon for which there is a line containing a side of the polygon that also contains a point in the interior of the 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. A polygon with all congruent sides. A triangle with all angles congruent. A convex polygon in which all of the sides are congruent and all of the angles are congruent. The sum of the lengths of the sides of a polygon. 4 4 4 4+4+4=12 Perimeter The distance around a circle The number of square units needed to cover a surface. 6 3 3x6=18 Area Polyhedron Face Edge Vertex Prism Base Pyramid Cylinder Cone Sphere Regular Polyhedron Platonic Solid Surface Area Closed three-dimensional figures made up of flat polygonal regions. The flat regions formed by the polygons and their interiors called faces. Pairs of faces intersect in segments called edges. Points where three or more edges intersect are called vertices. The flat surface of a polygon. A line that connects two nodes in a network. Edge The intesection of three edges of a polyhedron. Vertex A solid with thew following characteristics:
1. Two faces, called bases, are formed by congruent polygons that lie in parallel planes.
2. The faces that are not bases, called lateral faces, are formed by parallelograms.
3. The intersections of two adjacent lateral faces are called lateral edges and are parallel segments. The two parallel congruent faces of a polyhedron. Bases A solid with the following characteristics:
1. All of the faces, except one face, intersect at a point called the vertex.
2. The face that does not contain the vertex is called the base and is a polygonal region.
3. The faces meeting at the verex are called lateral faces and are triangular regions. A figure with bases that are formed by congruent circles in parallel planes. A solid with a circular base, a vertex not contained in the same plane as the base, and a lateral surface area composed of all points in the segments connecting the vertex to the edge of the base. In space, the set of all points that are a given distance from a given point, called the center. A polyhedron in which all of the faces are regular congruent polygons. The five regular polyhedra:
tetrahedron, hexahedon, octahedron, dodecahedon, or icosahedron. The sum of all faces and side surfaces of a three- dimensional figure. l h b Volume A measure of the amount of space enclosed by a three-dimensional figure. l h b V=bwh S.A.=2bh + 2bw + 2hw