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How to Draw Inter-Lines

Perpendicular Lines

Using a ruler and compass, we can draw perpendicular lines (shown below). Perpendicular lines are essentially line segments that meet at a right angle. We see examples of this all around us, for example: the sides of a set square or rectangle, the arms of a clock and even the corners of the blackboard.

Two intersecting lines are said to be perpendicular if they form a 90 degree angle with each other. The product of their slopes must be -1.

However, it is important to note that not all lines are perpendicular. Parallel lines, by definition, do not intersect and are coplanar. Skew lines are non-coplanar and do not intersect. Therefore, they cannot be perpendicular to each other. Intersecting lines are able to form a variety of angles, but they are never perpendicular. Perpendicular lines must be a perfect 90 degree angle. This is what defines them as such. If they are not, they can be referred to as parallel or intersecting.

Intersecting Lines

Intersecting lines are any two lines that cross each other. This can be useful in a number of different ways, including when working with maps and coordinates or in art.

In order for two lines to intersect, they must form a right angle at their point of intersection. This is true regardless of their slopes, and it is important to remember when interpreting geometric shapes.

There are many examples of intersecting lines in the real world. Some common examples include the ten yard lines on a football field or the rails of a railway track. However, it is also possible for two parallel lines to never intersect; these are known as non-intersecting lines.

Parallel Lines

Whenever you see parallel lines, like those running along your neighborhood streets or on your notebook paper, they never meet, merge or diverge. This means that they are coplanar (exist in the same plane).

When a transversal intersects two parallel lines, the angles formed are congruent or supplementary. For example, the pair of interior angles that share a common ray, like those shown in the diagram below, are equal. Angles on the opposite sides of the transversal, such as those between line a and line b, are also supplementary.

If a line has the same slope as another line, it is parallel to that line. The slope of a line can be determined by its equation, which is usually written as y = mx + b, where m represents the slope or gradient and b is the y-intercept. The value of m determines how steep the line is. The values of m for parallel lines are always the same, but their y-intercepts are not the same.

Straight Lines

In geometry, straight lines are one-dimensional, uncurved and can be either vertical, horizontal, or oblique. They divide the plane into two parts, if they are horizontal, above and below; or left and right, if they are vertical.

When two parallel lines meet, they form a pair of vertical angles that are opposite each other and share a common vertex at the point of intersection. This is called a linear pair, and the sum of these adjacent angles always equals 180°.

The slope of a line can be described in many ways, but the most useful way is to use the equation of a straight line. There are also other ways to describe a straight line, but these descriptions all represent the same straight line. For example, a slope can be described as the ratio of the distance traveled by the line to its change in elevation. This ratio is also known as the "rise over run" of a straight line.