[Maths Class Notes] on Construction of Perpendicular Lines Pdf for Exam

When two lines intersect each other to form right angles, these lines are called perpendicular to each other. Perpendicular lines lie on the same plane, which means that they are coplanar and intersect at the right angles. Therefore, it means that if you have two lines which are perpendicular to each other, these lines would be at right angles and vice versa. By using a ruler and a compass you can easily construct a line perpendicular to the other that passes through a point which lies on that line. In this article, we will learn about the construction of perpendicular lines step by step in detail.

Construction of Perpendicular Lines

Before you get into the construction procedure of the perpendicular lines, you must know about the construction of perpendicular lines in brief. The first step for constructing the line segment is that you have to draw the line segment for the given measurement. Then you need to mark the point on the line and then place the compass on that particular given point. Next, you need to draw the arc across the given line on either side. Now, without adjusting the compass, draw one more arc. You should note that when a perpendicular bisector is drawn for the given line segment, the division of the line segment would give you the equal measures on both the sides of that line.

Steps for Construction of Perpendicular Lines

Go through the following steps to draw a perpendicular line.

1. The first step for the construction of perpendicular lines is placing the compass on the given point (point P according to the diagram here). Next, draw an arc across the line on both the sides of the given point. Make sure that you do not adjust the compass width when you draw the second arc.

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2. From both the arcs on the line, draw another arc on the opposite side of the line you have drawn from the given point P in a way that the two new arcs intersect.

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3. Then use your ruler for joining the given point P to the point where the arc is intersecting at the point Q.

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Hence you can say that PQ is perpendicular to the line AB. 

You can also write it as PQ ⟂  AB

Constructing a Perpendicular Line Through a Point on the Line

Follow the following steps for constructing a perpendicular line through a point on the line.

1. First, you need to place your compass on the point given (point P here). Then draw an arc across the line on either side of this point on the line. Make sure that you are not adjusting the compass width while you are drawing the second arc.

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2. The next step is opening your compass in a way that it is wider than the distance from either of the arcs to the point P. Then place the compass on either of these arcs and draw an arc above or below the given point P in a way that the two new arcs intersect.

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3. Next, use your ruler for joining the point P at the point Q, where the arcs are intersecting.

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Construction of Perpendicular Lines with Example

Use the diagram given below to construct a perpendicular line to the given line AB that passes through the point C.

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Solution

1. First place your compass on the point Cand use any width for drawing an arc which intersects the line AB two times.

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2. Then, place your compass at both points A and B such that the arcs intersect. At each point, make an arc below the line AB. And lastly, label this intersection of both the arcs as D and connect D to the point C. The perpendicular line would look like this.

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