Mathematics

Lines and Types in Mathematics

len Alfred Ajibola - Fri, 12th July, 2019 @ 12:20 PM

Topics in Mathematics

Angles: Type of angles based on degree measurement Angle Pairs: Types of angle pairs Conversion of Number Bases explained with examples Angles: What are Angles? Categories of Angles Lines and Types in Mathematics Number Base System - Table showing the Number Bases with explanations Mathematics Scheme of Work, SS1, 3rd Term Mathematics Scheme of Work, SS1, 2nd Term Mathematics Scheme of Work, SS1, 1st Term Trigonometry - Sine, Cosine and Tangent explained with worked examples Quadratic Equation - Factorization of Quadratic Equation Algebra - Explanation and Worked Examples on Algebra


Academic Questions in Mathematics

Please click here to see all Questions and Answers

Decagon - Len Academy

What type of polygon is shown in the above image?

  • A. Nonagon

  • B. Decagon

  • C. Octagon

  • D. Hexagon

  • E. Hepagon

  • F. Pentagon

Which of the following is not part of a circle?

  • A. Section

  • B. Sector

  • C. Segment

  • D. Semicircle

  • E. Secant

  • F. Center

Acute Angle - Len Academy

What angle is shown in the above image?

  • A. Complementary

  • B. Supplementary

  • C. Acute

  • D. Obtuse

  • E. Reflex

  • F. Straight

An angle greater than 90o but less than 180o is termed _____.

  • A. Complementary

  • B. Supplementary

  • C. Acute

  • D. Obtuse

  • E. Reflex

  • F. Straight

Factorize 12a2 - 20a + 3

  • A. (6a - 1)(2a - 3)

  • B. (6a - 1)(2a + 3)

  • C. (6a + 1)(2a - 3)

  • D. (6a + 1)(2a + 3)

  • E. (-6a + 1)(2a - 3)

  • F. (-6a + 1)(2a + 3)

Simplify 10ab + 7ab

  • A. 17ab2

  • B. 17a2b2

  • C. 3ab2

  • D. 3a2b2

  • E. 17ab

  • F 3ab

Which of the following is not a type of angle?

  • A. Right angle

  • B. Left Angle

  • C. Acute Angle

  • D. Complete Angle

  • E. Straight Angle

  • F. Reflex angle

Two lines that can never meet each other are best considered as _____ lines.

  • A. straight
  • B. vertical
  • C. horizontal
  • D. parallel
  • E. oblique
  • F. perpendicular



Lines in Mathematics:

Lines are quite important in mathematics because having a good understanding of them would help students to better understanding angles.

Please read on Angles and Types of Angles here.


Every form of line must begin from a point. In fact, a line can only be drawn within two different points. You can think of a point as a location. It has no length, depth or width. It is generally represented as a dot.

Note: A point is not necessarily a dot. A dot shows you where the point (location) really is.

As an instance, Below are five different points represented by a dot.

. . . . .


A line can be defined as the path between two points.

A line usually have a length but may have no width.


Lines are generally put into two categories in mathematics. Every other type of line will lie within these 2.

The two categories of lines are straight lines and curved lines.

Please read on the types of Line in technical drawings here.

 

  • Straight Line

When the path between two points are straight, then the line that is associated with the path is a straight line.

A straight line can be drawn in any direction. It could go from north to south or east to west.

The image below shows a straight line running from east to west.

EAST ______________________ WEST

 

Types of Straight Line

Below are types of straight line:


1. Horizontal Line

A horizontal line is a line that runs from left to right or east to west in a straight line.

 

2. Vertical Line

A vertical line runs from top to bottom or north to south in a straight line.

 

3. Perpendicular Line

The word perpendicular simply means “at right angles”.

Two lines are said to be perpendicular if they meet or cross each other at a right angle.

Note: A right angle is an angle at ninety degrees (90o).

Perpendicular Line - Len Academy

In the diagram above, you will observe that the line CD meets line AB at point E, which is at a right angle (90o). Line CD is therefore said to be perpendicular to line AB at point E.


Note the following from the above diagram:

  1. Line AB is a horizontal line.
  2. Line CD is a vertical line.
  3. If Line CD had met line AB at another angle; lets say at angle 45o, then we can correctly say that line CD meets line AB obliquely.
  4. Please read on trigonometry here.

 

4.Parallel Line

Two lines are considered to be parallel if they will never meet each other, no matter the length at which you extend them.

The diagram below show two parallel lines:

Parallel Lines - Len Academy

 

5. Oblique Line

Oblique lines are neither perpendicular nor parallel. They are slanted or tilted lines that will finally meet at some point, but not at a right angle (90o).

Oblique Lines - Len Academy


From the diagram above, the lines in:

  • Figure 1 is oblique
  • Figure 2 is perpendicular
  • Figures 3 and 4 are parallel

Note: Oblique lines are sometimes referred to as slanting lines.

 

  • Curved line

Curved Line - Len Academy

When the path between two lines isn’t straight, then such line can be said to be curved. Below is a curved line.

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Amazing facts in Mathematics

The opposite sides of a dice will always give a sum of seven

31,556,926 seconds makes one year

From 0 through 1000, the only number that has the letter 'a' in it is 'one thousand'

÷

The division symbol '÷' is actually called an obelus

Four is the only number in the English language that is spelt with the same number of letters as the number (4) itself

40 is spelt as forty and not 'fourty'. It is the only number that is spelt with letters arranged in alphabetical order

An odd number is a number that cannot be divisible by 2.

Every odd number has an 'e' in its spelling. They include:

  • One
  • Three
  • Five
  • Seven
  • Nine

555 in Thailand sounds like 'hahaha'. This is because the number '5' means 'ha' in Thailand

In mathematics, 10! means 10 factorial. Below is its calculation:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

Interestingly, 3628800 seconds is the same as 42 days

42 days is the same as 6 weeks

We can therefore say that 10! equals 6 weeks or 3628800 seconds in mathematics

When you multiply 111,111,111 by 111,111,111; the result equals 12,345,678,987,654,321


Notable points in Mathematics

Let's use algebra to explain the simple statement below:

I am a number. When you subtract 3 from me, the result is 9. what number am I ?

Of course we know the answer is 12. You probably guessed it from your mind because it was that simple. The truth is, We could have a much more complicated statement of such; and that is where algebra comes into play.

Now, to apply algebra in the above statement, we use letters or alphabets to represent the unknown number(s). So using algebra, we can write:

  • Let the number be y

  • y - 3 = 9

  • y = 9 + 3

  • y = 12

Please read more on algebra here

Sides of a right angle triangle - Len Academy

 

The image above shows a right angled triangle. The angle of the above right triangle is denoted as θ. Below are some points to note:

Hypotenuse is always the longest side of the triangle.

Opposite is the side opposite the angle (θ)

Adjacent is the shorter side next to the angle (θ)

Each of Sin θ, cos θ and tan θ are the ratio of sides of the right triangle. They are calculated by using the formula (margic word) sohcahtoa:

Sohcahtoa - Len Academy

soh

Sin θ = Opposite/Hypotenuse

cah

Cos θ = Adjacent/Hypotenuse

toa

Tan θ = Opposite/Adjacent

Please read more on sine, cosine and tangent here

Circumference of a Circle - Len Academy

Circumference in mathematics means the distance around the edge of a circle (or a another curved surface).

Circumference is to circle or any other curved surface

Perimeter of a Rectangle - Len Academy

Perimeter means the distance around a square or rectangle or polygon.

Perimeter is to square or rectangle or polygon