The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight “sides” meeting at one place.

Intersecting lines are two or more lines that are coplanar to each other and meet at a common point. The three pairs of lines shown above are examples of intersecting lines.

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

Intersecting Lines A pair of lines, line segments or rays are intersecting if they have a common point. This common point is their point of intersection. For example, two adjacent sides of a sheet of paper, a ruler, a door, a window and letters.

Three lines in a plane can intersect in exactly two points if two lines are parallel and the third is not, as shown in Figure 3 below.

Concurrent Line Segments and Rays When three or more line segments, intersect each other at a single point, then they are said to be concurrent line segments.

Two planes parallel to the same line are parallel. (to each other Two lines perpendicular to the same plane are parallel. If a line is oblique to a plane, it is perpendicular to exactly one line in the plane.

No Solutions, 1 Solution or Infinite Solutions Like systems of linear equations, the solution of a system of planes can be no solution, one solution or infinite solutions.

Properties of Intersecting Lines The intersecting lines (two or more) always meet at a single point. The intersecting lines can cross each other at any angle. This angle formed is always greater than 0∘ and less than 180∘. Two intersecting lines form a pair of vertical angles.

Whenever two straight lines intersect, they form two sets of angles. The intersection forms a pair of acute and another pair of obtuse angles. The absolute values of angles formed depend on the slopes of the intersecting lines.

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

A line is defined by two points. Saying there are an infinite number of points on the line does not mean they make up the line; it means there are an infinite number of pairs of points that define the same line. If the parallel lines intersect or not , if both the lines in the same plane ? No they don’t.

A ray is a line with an endpoint that extends infinitely in one direction. example : sun rays : The light originates from the sun, and its path extends infinitely (assuming there’s nothing to block it). We call this a sun ray because it has only one endpoint (the sun) and extends infinitely in one direction.

A point is defined as a location in any space and is represented by a dot (.). It does not have any length, height, shape, or size. It marks the beginning to draw any figure or shape and is labeled with capital letters. Line. A series of points connected by a straight path is defined as a line.

Examples could be triangles, squares, rectangles, lines, circles, points, pentagons, stop signs (octagons), boxes (prisms, or dice (cubes). Examples of a plane would be: a desktop, the chalkboard/whiteboard, a piece of paper, a TV screen, window, wall or a door.

What is a real world example of a line? Real-world examples of line segments are a pencil, a baseball bat, the cord to your cell phone charger, the edge of a table, etc. Think of a real-life quadrilateral, like a chessboard; it is made of four line segments.

The concepts of points, lines, planes, line segments, and rays are crucial for creating a great foundation on which to understand Geometry. The symbolism is particularly important. It is represented by a line with two arrow heads. Through any two points there is exactly one line.

symbol ∼

To symbolize parallel lines in geometry, we use two vertical lines (or slightly slanted lines), like this:

1. AT ∥ UP.
2. AT // UP.
3. Our line is established with the slope-intercept form, y = mx + b y = m x + b .
4. 3x − y = −4.
5. 3x − y − 3x = −4 −3x.
6. −y = −4 − 3x.
7. y = 3x + 4.
8. y = 3x − 5.