Definitions of Key Geometric Terms A quick review of material covered in Math A La Salle Academy, Mrs. Masullo.

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.