Where Do Orthogonal Lines Meet
What Is Perpendicular?
Two singled-out lines intersecting each other at xc°, or a right angle, are called perpendicular lines.
Instance:
Here, AB is perpendicular to XY because AB and XY intersect each other at ninety°.
Non-Example:
 |  |  |
| The 2 lines are parallel and practice not intersect each other. They tin can never exist perpendicular to each other. | The two lines are intersecting each other at an astute bending. Then, they are not perpendicular. | The lines are non intersecting each other at right angles. |
Perpendicular Symbol
Perpendicular lines are represented past the symbol '⊥'. Suppose, m and n are two lines intersecting each other at 90°, then they are perpendicular to each other and are represented as m ⊥ n. The signal of intersection of perpendicular lines is called the foot of the perpendicular.
Properties of Perpendicular Lines
- These lines ever intersect at correct angles.
- If two lines are perpendicular to the aforementioned line, they are parallel to each other and volition never intersect.
- Adjacent sides of a square and a rectangle are always perpendicular to each other.
- The sides of the correct-angled triangle enclosing the right angle are perpendicular to each other.
Real Life Examples
We tin can observe many perpendicular lines in real life.
Some examples are the sides of a set square, the arms of a clock at certain times of the day, the corners of the blackboard, a window, and the Red Cross symbol.
Departure betwixt Perpendicular Lines and Parallel Lines
| Perpendicular Lines | Parallel Lines |
| Perpendicular lines are lines that intersect at a 90° angle. | Parallel lines are lines that are always the same distance apart. Parallel lines never intersect. |
| The symbol used to represent a perpendicular line is "⊥". | The symbol used to represent a parallel line is "||". |
| Example: The corner of the postcard | Case: Railway tracks |
| The corner of a ruler | The edges of a ruler |
Construction of Perpendicular Lines
Nosotros can draw perpendicular lines for a given line in two ways.
- Using a protractor
- Using a compass
Drawing a perpendicular line using a protractor
Step 1: Allow chiliad be the given line and A the given indicate on it.
Pace two: Place the protractor on the line m such that its baseline coincides with m, and its center falls on A.
Step 3: Marker a indicate B against the 90-degree mark on the protractor.
Footstep 4: Draw a line northward passing through A and B.
Then line m ⊥ line due north at A.
Drawing a perpendicular line at a given indicate on a line using a compass
Pace 1: Identify a compass tip on the given bespeak A. Take an appropriate radius and depict an arc on either side of the given point.
Step 2: Stretch the compass wider. Place the compass tip on the new points and brand a minor arc above the given line. The two new arcs will intersect.
Pace iii: Use the ruler to bring together the given betoken A and point B where the arcs intersect.
Solved Examples on Perpendicular
Example 1: Land whether a given ready of lines are perpendicular or parallel.
 (a) | (b)  |
(c)  | (d)  |
Solution:
- Parallel lines
- Perpendicular lines
- Perpendicular lines
- Parallel lines
Example two: Write a relation betwixt the line segments indicated past the arrow in each shape.
Solution:
- AB ⊥ AE
- PQ || SR
- PQ || NM
- AB ⊥ AD
Example 3: The diagonals of a rhombus are perpendicular to each other. How many right angles are formed at the intersection?
Solution:
Since the lines Ac and BD intersect each other at ninety degrees, there are 4 right angles at the intersecting signal.
∠AED = ∠DEC = ∠CEB = ∠BEA = 90 degrees
Example 4: Name some two-dimensional shapes that have perpendicular lines.
Solution:
Where Do Orthogonal Lines Meet,
Source: https://www.splashlearn.com/math-vocabulary/geometry/perpendicular
Posted by: stanfordparrall.blogspot.com
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