Which Shape Has Perpendicular Sides

What Is Perpendicular?

Two distinct lines intersecting each other at ninety°, or a correct angle, are called perpendicular lines.

Example:

Here, AB is perpendicular to XY because AB and XY intersect each other at xc°.

Non-Example:

The two lines are parallel and do not intersect each other. They can never exist perpendicular to each other.	The two lines are intersecting each other at an acute angle. So, they are not perpendicular.	The lines are not intersecting each other at right angles.

Perpendicular Symbol

Perpendicular lines are represented by the symbol '⊥'. Suppose, m and northward are two lines intersecting each other at 90°, then they are perpendicular to each other and are represented as chiliad ⊥ n. The point of intersection of perpendicular lines is called the foot of the perpendicular.

Properties of Perpendicular Lines

• These lines always intersect at right angles.
• If two lines are perpendicular to the aforementioned line, they are parallel to each other and will never intersect.

• Adjacent sides of a square and a rectangle are always perpendicular to each other.

• The sides of the right-angled triangle enclosing the right bending are perpendicular to each other.

Real Life Examples

We can notice many perpendicular lines in existent life.

Some examples are the sides of a set square, the arms of a clock at certain times of the twenty-four hour period, the corners of the blackboard, a window, and the Red Cross symbol.

Difference between 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 ever 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

Example: Railway tracks

The corner of a ruler

The edges of a ruler

Construction of Perpendicular Lines

We can draw perpendicular lines for a given line in two ways.

• Using a protractor
• Using a compass

Drawing a perpendicular line using a protractor

Pace 1: Let thou exist the given line and A the given indicate on it.

Step ii: Place the protractor on the line thou such that its baseline coincides with m, and its eye falls on A.

Step three: Mark a point B confronting the ninety-degree marking on the protractor.

Step 4: Draw a line due north passing through A and B.

Then line g ⊥ line n at A.

Drawing a perpendicular line at a given signal on a line using a compass

Step 1: Place a compass tip on the given bespeak A. Have an appropriate radius and draw an arc on either side of the given bespeak.

Step two: Stretch the compass wider. Identify the compass tip on the new points and make a small-scale arc above the given line. The two new arcs will intersect.

Step iii: Utilize the ruler to join the given betoken A and point B where the arcs intersect.

Solved Examples on Perpendicular

Instance 1: Land whether a given set of lines are perpendicular or parallel.

(a)	(b)
(c)	(d)

Solution:

1. Parallel lines
2. Perpendicular lines
3. Perpendicular lines
4. Parallel lines

Case 2: Write a relation between the line segments indicated by the arrow in each shape.

Solution:

1. AB ⊥ AE
2.  PQ || SR
3. PQ || NM
4. AB ⊥ Advertising

Instance 3: The diagonals of a rhomb 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 90 degrees, there are 4 right angles at the intersecting point.

∠AED = ∠Dec = ∠CEB = ∠BEA = 90 degrees

Example four: Name some 2-dimensional shapes that have perpendicular lines.

Solution:

Which Shape Has Perpendicular Sides,

Source: https://www.splashlearn.com/math-vocabulary/geometry/perpendicular

Posted by: eppersonhisdon.blogspot.com

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