Perpendicular Line

Perpendicular Line

Two straight lines can intersect each other and four angles are formed at the point of intersection. When two lines intersect and the angles formed at the point of intersection are all 90 degrees than these two lines are perpendicular lines. In other words, any two lines which make an angle of 90 degrees at the point of intersection are perpendicular. We can observe a lot of perpendicular lines around us in our daily lives. One common example is the edges of the floor and walls in the room which meet at the corner point of the room.

Properties of Perpendicular Line

  • Perpendicular lines are two straight lines that meet or intersect each other to form an angle of 90 degrees at the point of meeting or intersection.
  • Perpendicular lines always come in pairs each of which is perpendicular to the other line.
  • Two perpendicular lines form four right angles (90 degrees) at the point of intersection.
  • A line can have more than one line perpendicular to it.

How to Identify Perpendicular Lines

A perpendicular line is a straight line that makes an angle of 90 degrees with another line at their meeting point. An angle of 90-degree measurement is also called a right angle. So we can say, two perpendicular lines meet to form a right angle. A right angle is often denoted by a small square at the point of intersection of two perpendicular lines. There is always a pair of perpendicular lines.
For example line AB and line, CD intersects at a point O and forms a right angle at the meeting point. So AB and CD are perpendicular to each other.

Shapes of Perpendicular Lines

Various geometrical shapes have perpendicular lines. A square and a rectangle have adjacent sides that are perpendicular to each other. A right-angle triangle has a right angle opposite to the largest side so the two sides adjacent to the right angle are perpendicular lines. An easy way to identify two perpendicular lines is that they form an ‘L’ shape in a figure.

Parallel Line

Two or more straight lines lying on a plane but can never meet or intersect are called parallel lines. The lines can be of the same or different lengths or can be extended in any direction but they never meet. So there is no question of any angle formed between two parallel lines. An important property of parallel lines is that the perpendicular distance between two points on any two parallel lines is always equal. In other words, two parallel lines are equidistant from each other. We can observe parallel lines in our day-to-day lives such as zebra crossings on the road, two opposite sides of a wall, two sides of a ruler, etc.

Properties of Parallel Lines

  • A pair of parallel lines are always at the same distance apart from each other. 
  • Parallel lines never meet or intersect even if they are extended in either direction. 
  • Two parallel lines when cut by a third line called transversal, the alternate interior angles formed are equal, and alternate exterior angles formed are also equal.
  • In two parallel lines when cut by a third line, the consecutive interior angles on the same side of the transversal will be supplementary angles. 

Equation of Parallel Lines

The equation of a straight line can be denoted in the form y = mx + b where m is the slope of the line that indicates the inclination or steepness of the line. It is important to note that the slope of parallel lines is equal.
For example, y = 3x + 10 and y = 3x + 25 are two parallel lines as both of them have the same slope value which is 3. 

If you want to learn more about maths concepts in a detailed manner, visit Cuemath to book a free session. 

By Michael Caine

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