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.