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CAT Basic Terms and Definitions of Lines and Angles - Practice Questions & MCQ

Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

Concepts Covered - 1

Basic Terms and Definitions of Lines and Angles

Basic Terms and Definitions

The two simplest objects in geometry are points and lines

Point: A point is a coordinate that marks a position in space (on a number line, on a plane or in three dimensions or even more) and is denoted by a dot. Points are usually labelled with a capital letter. 

Line: A line is a continuous set of coordinates in space and can be thought of as being formed when many points are placed next to each other. Lines can be straight or curved, but are always continuous. This means that there are never any breaks in the lines. The endpoints of lines are labelled with capital letters. 

Lines are labelled according to the start point and end point. We call the line that starts at a point A and ends at a point B, AB. Since the line from point BB to point A is the same as the line from point A to point B, we have that AB=BA.

Line Segment: A part (or portion) of a line with two end points is called a line-segment.

If three or more points lie on the same line, they are called collinear points; otherwise they are called non-collinear points.

Ray: A ray is a directed line segment. It consists of one point on a line and all points extending in one direction from that point. The first point is called the endpoint of the ray. We can refer to a specific ray by stating its endpoint and any other point on it. 

Note that the line segment AB is denoted by \overline{\text{AB}} and its length is denoted by AB. The ray AB is denoted by \overrightarrow{\text{AB}} and a line is denoted by \overleftrightarrow{\text{AB}}.

However, in this chapter, we will not use these symbols, and will denote the line segment AB, ray AB, length AB and line AB by the same symbol, AB. The meaning will be clear from the context.

Angle: An angle is the union of two rays having a common endpoint. The endpoint is called the vertex of the angle, and the two rays are the sides of the angle.

The angle in below figure is formed from \overrightarrow{\text{ED}} and \overrightarrow{\text{EF}}. Angles can be named using a point on each ray and the vertex, such as angle DEF, or in symbol form \angle DEF.

Angle creation is a dynamic process. We start with two rays lying on top of one another. We leave one fixed in place, and rotate the other. The fixed ray is the initial sideand the rotated ray is the terminal side. In order to identify the different sides, we indicate the rotation with a small arrow close to the vertex as in figure given below.

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