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.
• A statement that can be proven by deductive reasoning.
Theorem
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 180.
• Complementary and supplementary angles can be adjacent or nonadjacent.
Supplementary angles
• Two angles whose sum in degree measures is 90.
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.
Median
• The line segment drawn from any vertex of an object , perpendicular to the opposite side.
Altitude
• 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.
• 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.
Parallelogram
Trapezoid
• A quadrilateral that has only one pair of parallel sides, called bases. The non-parallel sides are the legs of the trapezoid.
• In an ISOSCELES trapezoid, the legs are congruent.