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Download Definitions of Key Geometric Terms
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Definitions of Key Geometric Terms A quick review of material covered in Math A La Salle Academy, Mrs. Masullo Point • A position in space. • A point has no dimensions. • A point is represented by a dot and named with a capital letter. Line • An infinite set of points extending in two directions. • A line is named using two of its points, such as AB with a double arrow above it, or by using a single lowercase script letter. Plane • A set of points extending infinitely in all directions. • A plane is named with a capital letter. Collinear • Points that are contained on the same line. Coplanar • Points that are contained on the same plane. Postulate • A statement that is assumed to be true. Theorem • A statement that can be proven by deductive reasoning. Congruent • If two figures are congruent, they have the same size and shape. • The symbol for congruence is meaning that the figures are equal (=) in measure and similar (~) in shape. Angle • The union of two rays that share a common endpoint. • The two rays form the sides of the angle and the intersection of the two rays is the vertex of the angle. • An angle can be named by a capital letter located at its vertex; by three capital letters, the middle letter being the vertex; by a lowercase letter or a number placed inside the angle. Bisector • A bisector of an angle is a ray whose endpoint is the vertex of the angle, which divides the angle into two congruent angles. • A bisector of a line segment is the line (or part of a line) that intersects the segment at its midpoint, dividing the segment into two congruent line segments. Adjacent Angles • Two coplanar angles that share a common vertex and a common side, but have no interior points in common. Complementary angles • Two angles whose sum in degree measures is 90. Supplementary angles • Two angles whose sum in degree measures is 180. • Complementary and supplementary angles can be adjacent or nonadjacent. A linear pair of angles • A pair of two adjacent angles whose sum is a straight angle. Line Segment • The set of points containing two points on a line, called the endpoints of the line segment, and all points on the line between the endpoints. • Because a line segment has two endpoints, it has a definite length. Midpoint • The midpoint of a line segment is the point that divides the segment into two congruent segments. Perpendicular lines • Two lines that intersect to form right angles. Perpendicular bisector • A line (or part of a line) that is perpendicular to the line segment, intersecting the line segment at its midpoint. Polygon • A closed figure formed by coplanar line segments that are joined at their endpoints. • A REGULAR polygon is both equilateral and equiangular (all sides and all angles are congruent). Triangles classified by angles • A polygon that has exactly three sides. • An ACUTE triangle has three acute angles (each measures < 90 deg.) • A RIGHT triangle has one right angle and two acute angles. The sides that form the right angle are called legs, and the side opposite the right angle is the hypotenuse. • An OBTUSE triangle has one obtuse angle (>90 deg.) and two acute angles. Triangles classified by sides • An EQUILATERAL triangle has three congruent sides. An equilateral triangle is also equiangular, so it is a regular polygon. • An ISOSCELES triangle has at least two congruent sides. The two congruent sides are called legs, and the third sides is called the base. Base angles are always congruent. • A SCALENE triangle has no congruent sides. Altitude • The line segment drawn from any vertex of an object , perpendicular to the opposite side. Median • A line segment drawn from any vertex of an object to the midpoint of the opposite side. Quadrilateral • A four-sided polygon. The most important quadrilaterals that we will study are parallelograms and trapezoids. Parallelogram • A quadrilateral whose opposite sides are parallel. • A rectangle is a parallelogram containing four right angles. • A rhombus is a parallelogram with four congruent sides. • A square is a rhombus with four right angles, or a rectangle with four congruent sides. Trapezoid • A quadrilateral that has only one pair of parallel sides, called bases. The nonparallel sides are the legs of the trapezoid. • In an ISOSCELES trapezoid, the legs are congruent.