Geometry is a very important and most interesting topic for Students. Children feel excited to practice the problems because it deals with various interesting measuring instruments like scale, compass, and a set of squares, etc to solve. Perpendicular lines are an important concept to solve various complex problems in your higher studies.
To understand how to construct a perpendicular line, first, you need to be familiar with lines, types of lines, and perpendicular lines. A line has infinite points and has no starting point and ending point. In this article, you will get to know about perpendicular lines and the Construction of Perpendicular Lines by using a Protractor with few examples in learning and practicing accurately.
Perpendicular Lines – Definition
Perpendicular lines are the lines that are formed when two lines meet and intersect at each other at a right angle or 90 degrees and marked a little square between two lines where they intersect. Perpendicular lines are represented by a symbol ‘⊥’. For example, if a line AB is perpendicular to the line CA we write it as AB ⊥ CA.
How to Draw a Perpendicular Line with a Protractor?
To construct a perpendicular line we have two methods to follow. One is by using a Compass and Straight Edge and another method to follow is by using a protractor. Here, in this article children will know how to construct a perpendicular line using a protractor in detail. Let’s discuss the Construction of Perpendicular Lines by using a Protractor through the following steps:
Step 1: Draw a straight line and place the baseline of the protractor on the center of the drawn line such that its label the center is as point M. Adjust the protractor so that its base settles exactly over the line drawn.
Step 2: Mark a point as P at 90° of the protractor. This 90° is at the center of the protractor where it forms a perpendicular line by joining a line from point P to point M. Thus, you get a right angle and a perpendicular line.
Step 3: Now, remove the protractor and draw a straight line by using a straight edge of the protractor to point P from point M. This line is a perpendicular line to the line drawn, through the given point on the line and forms a right angle or 90°.
Constructing Perpendicular Lines using a Protractor Examples
Example 1:
How to draw a perpendicular line by the line segment AB from point B and point P is perpendicular with the help of a protractor?
Solution:
Now, to draw a perpendicular line children have to follow the above steps.
We have a given line segment AB.
Step1: Draw a line segment AB and place the center of the protractor at point B because we have to draw a perpendicular line from Point B.
Step2: Now, mark the point P at 90° to get a perpendicular line.
Step3: Remove the protractor and draw a straight line from point B to point P with the help of a ruler to get a perpendicular line where it forms a right angle.
Now, line AB is perpendicular to line BP. Hence, AB ⊥ BP
Example 2:
Draw a perpendicular line by forming two line segments where they intersect each other and forms a right angle.
Solution:
First, let us draw a line segment AB.
Keep the protractor on the line segment AB and place the protractor on the center of the line segment and mark the center as point D.
Now, mark the point exactly at 90° of the protractor label the point as C, and remove the protractor.
Draw a straight line by a ruler from point D to point C where both the lines intersect each other at a point and forms a perpendicular line at 90°.
Hence, AB ⊥ CD.
FAQs on Construction of Perpendicular Lines by using a Protractor
1. How do you represent a perpendicular line?
If two intersect each other and form a right angle is known as a perpendicular line. The symbol we used to represent a perpendicular line between the lines is ⊥.
2. What are the types of perpendicular lines to construct?
The methods we used to construct a perpendicular line are by using a compass and a ruler, by using a protractor and a ruler.
3. How do you notice the lines are perpendicular or not?
If the slope of the lines is the same then they are parallel lines and if the slope of the line is negative reciprocal of the second line, then they are a perpendicular line.
4. What is the slope of a perpendicular line and the type of angle the perpendicular lines form?
The slope of two perpendicular lines is negative reciprocal of each other. If a line is perpendicular to a line that has a slope of m, then the slope of a line is -1/m. Perpendicular line forms an angle and intersects at 90 degrees.