Construction of Perpendicular to a Line through a Point on it

# Construction of Perpendicular to a Line through a Point on it Video Lecture | Mathematics (Maths) Class 6

## Mathematics (Maths) Class 6

134 videos|325 docs|42 tests

## FAQs on Construction of Perpendicular to a Line through a Point on it Video Lecture - Mathematics (Maths) Class 6

 1. What is the construction of a perpendicular to a line through a point on it?
Ans. To construct a perpendicular to a line through a point on it, follow these steps: 1. Draw the given line and mark the point on it where the perpendicular is to be constructed. 2. From the marked point, draw a line segment of any convenient length that forms an acute angle with the given line. 3. Using a compass, construct an arc with the same radius as the line segment drawn in the previous step, centered at the marked point. 4. Without changing the compass width, draw two arcs intersecting the given line on both sides. 5. Join the intersection points with the marked point. This line will be perpendicular to the given line through the marked point.
 2. What are the properties of a perpendicular line?
Ans. The properties of a perpendicular line are as follows: - Two lines are perpendicular if they intersect at a right angle (90 degrees). - Perpendicular lines have slopes that are negative reciprocals of each other. - The product of the slopes of two perpendicular lines is -1. - Perpendicular lines form four right angles at their point of intersection. - If a line is perpendicular to one of two parallel lines, it is perpendicular to the other parallel line as well.
 3. How do you prove that a line is perpendicular to another line?
Ans. To prove that a line is perpendicular to another line, you can use one of the following methods: - Show that the slopes of the two lines are negative reciprocals of each other. - Show that the product of the slopes of the two lines is -1. - If the lines are given in the form of equations, substitute the coordinates of a point on one line into the equation of the other line. If the result is -1, the lines are perpendicular. - Use the congruence of corresponding angles formed by the lines to prove that they intersect at a right angle.
 4. Can a line be perpendicular to itself?
Ans. No, a line cannot be perpendicular to itself. Perpendicular lines are defined as two lines that intersect at a right angle, forming four right angles. If a line were to be perpendicular to itself, it would imply that it intersects at a right angle with itself, which is not possible.
 5. Can two lines be perpendicular if they are parallel?
Ans. No, two lines cannot be perpendicular if they are parallel. Perpendicular lines intersect at a right angle, while parallel lines never intersect. Therefore, if two lines are parallel, they cannot intersect at a right angle, and hence, they cannot be perpendicular to each other.

## Mathematics (Maths) Class 6

134 videos|325 docs|42 tests

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