In Geometry, two lines are said to be perpendicular to each other if they lie in the same plane and meet each other at right angles (90 degrees). Both lines are considered perpendicular to each other.
Diagram showing perpendicular lines
In the above diagram, line AB intersects line PQ at right angles, hence the two lines are perpendicular to each other.
Properties of pendicular lines
Perpendicular lines show the following properties:
1. If a line AB is perpendicular to another line PQ, then it is also perpendicular to any line parallel to the line PQ.
2. When a line is perpendicular to another line then all the angles formed at the point of intersection are always right angles.
Whenever a linear pair of angles is congruent, the angles are always 90 degrees.
In the above figure, Lines AB and PQ intersect each other at point O. Angle AOP and Angle AOQ form a linear pair. Each angle is equal to 90 degrees and hence the angles are congruent.
All the four angles formed at the intersection of perpendicular lines are congruent.
How to construct perpendicular lines
You can construct a perpendicular line to a given line using a compass and ruler as follows:
- 1. Draw a straight horizontal line and mark two points P and Q on the line.
- 2. Take a compass and place it at one of the end points - P of the horizontal line.
- 3. Make an arc above and below the horizontal line.
- 4. Now place the compass at the other end point - Q of the horizontal line without changing the compass width.
- 5. From point Q, make an arc above and below the horizontal line.
- 6. The arcs made from the two end points of the line will intersect. Mark these points of intersection as A and B.
- 7. Draw a straight line AB joining the two intersecting points on the arc.
- 8. The lines AB and PQ are perpendicular to each other.
Perpendicular lines are used to calculate the distance from a point to a straight line, a curve or a plane.
Application of perpendicular lines
Perpendicular lines are used to find out distances.
1. When you need to calculate the distance from a point to a given line, the shortest distance from the point to the line is considered. This distance is determined by drawing a perpendicular from the point to the line.
2. In order to calculate the distance from a point to a curve, you can draw a perpendicular line from the point to the tangent line of the curve.
3. In order to calculate the distance from a point to a given plane, you can draw a perpendicular line from the point to the nearest point on the plane.
Perpendicular lines in polygons
There are different polygons which have perpendicular lines
1. In a right angled triangle, the two sides forming the right angle are perpendicular to each other.
2. The line showing the altitude of a triangle is perpendicular to the base of the triangle.
3. In quadrilaterals such as squares and rectangles, adjacent sides are always perpendicular to each other.
4. In a circle the diameter is perpendicular to the tangent of the circle.
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