Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 1.2 Informal Geometry and Measurement

Vocabulary “Undefined” terms Point:Location but no size. Represented by a dot. Usually named using upper case letter. No dimension Line: Has infinite length but no width. Has the quality of “straightness”. Named with lower case script letter or by identifying two points contained in the line with double arrow above. One-dimensional. Plane: Has infinite length and infinite width but no thickness. We use upper case letters to name planes. Two-dimensional.

Vocabulary Informal definitions A line segment is the portion of a line between two points. We name the segment using these two endpoints, showing a bar above the letters. No bar refers to the distance between the endpoints or the length of the segment. If we use a ruler to measure, we are only getting an approximation.

Vocabulary Informal definitions Three points are said to be collinear if they are on the same line. A-X-B will indicate points A, X, and B are collinear and X is between A and B. If B is a point on the segment AC, then B is a midpoint of segment AC if AB = BC. Two figures of the same shape and size are said to be congruent. 

Vocabulary Informal definitions An angle has two sides and a common point called the vertex. The angle can be named using the vertex only, or using points from one of each of the sides and the vertex – in that case the vertex is always written as the middle point. We measure angles using a protractor. The units are degrees. Always use .

Vocabulary Informal definitions If ÐABD is separated into two congruent angles ÐABC and ÐCBD then ÐABD has been bisected. Any angle measuring 180  is a straight angle. When a straight angle is bisected, the two angles formed are right angles.

Vocabulary Informal definitions Figures such as triangles and rectangles are named by listing their vertices. Adjacent vertices in the name imply that the line segment containing them are sides on the figure.  ABC rectangle WXYZ

Vocabulary Informal definitions A circle is the set of all points in a plane that are a given distance from a given point (called the center). Any line segment joining the center to a point on the circle is called the radius. (Plural radii) A part of a circle between any two of its points is called an arc.

Construction: Bisect a line segment Given: Segment AB Construct: M so that AM = MB (M is the midpoint of segment AB) Construction 2, p. 15 in text