Question

What is the perpendicular line theorem?

Answer 1

Hint: Whenever we are dealing with a pair of lines, there are three relationships which may be possible. First the lines can be parallel, second the lines can be perpendicular, or neither. Now what does parallel mean? When lines are parallel to each other, it means they will never intersect or touch/cross each other because they have the same slope, and are therefore always equidistant to each other from starting to end of the lines. But when lines are perpendicular, they intersect each other at right angles and because of that intersection, perpendicular lines have negative reciprocals slopes.

Complete step by step solution:
Perpendicular lines occur anytime, when two straight lines meeting with each other at $90$ degree are called perpendicular lines. Or we can say that when a straight line intersects with another straight line at an angle of $90$ degrees, they are said to be perpendicular to each other. Sometimes, you will see a little square in the corner of an angle to show it is perpendicular.
There are three basic theorems on perpendicular lines which we use to solve simple and complex problems on perpendicular. The theorems are:
Theorem1: If two lines intersect to each other and form a linear pair of congruent angles, the lines known as perpendicular. Here congruent angles are those angles which are equal to each other.

Theorem2: If two lines are perpendicular to each other, they will intersect to form four right angles.

Theorem3: If two sides of two adjacent acute angles are perpendicular to each other, the angles are called complementary angles. Acute angles are angles which are less than $90$ degrees and adjacent angles are angles that are besides to each other.

Note: As we explain above about the perpendicular lines it is useful in solving problems. There are many places around you where you can find perpendicular lines like corners of rooms, doors, parking lots, tennis, roadways, etc. it means all the rectangular and square shapes around you will have pairs of perpendicular lines.