Lines and angles

Lines and angles are the fundamental terms in geometry that serve as the subject’s foundation. A line is defined as a row of closely spaced dots that extends in 2 directions indefinitely. It only has one dimension, and that is its length. A line can be represented by a horizontal mark drawn on a piece of paper. An angle is a figure formed by two rays that intersect at a common endpoint. A protractor is used to measure them in degrees. Lines and angles are present in all geometry shapes.

Concept of Lines and angles

The ancient mathematicians invented the concept of lines to represent straight objects with no width or depth. An angle is a shape formed by the intersection of two line segments, lines, or rays, whereas lines are easier to understand. An angle is formed when two rays intersect in the same plane.

Lines

A line is a one-dimensional figure that extends in both directions indefinitely and has no width. It is made up of an infinite number of points that are close to each other. 

They are classified into 3 categories:

1. Intersecting Lines: Two lines are intersecting if they cross at the same point.
2. Parallel Lines: If two lines never intersect, they are said to be parallel.
3. Transversal line: A transversal line is a line that connects two or more lines at distinct points.

Lines’ Properties

• Lines are defined as a collection of an infinite number of points that are close to each other.
• They are infinitely long in both directions.
• They are one-dimensional, with no depth or thickness.

Angles

An angle is formed when two rays intersect at a point. Angles are commonly measured in degrees and denoted by the degree symbol “∘” which is a rotational measure.

They are classified into four categories:

1. Acute angle: When the angle measurement falls between 0 and 90 degrees.
2. Right angle: When the angle measurement is exactly 90 degrees.
3. Obtuse angle: When the angle measurement falls between 90 and 180 degrees.
4. Reflex angle: When the angle measurement falls between 180 and 360 degrees.

Angle Properties

• An angle is a geometric figure created when two lines intersect in the same plane.
• The lines that form an angle are known as its arms (sides), and the point where they meet is known as the angle’s vertex.

Lines and angles formula

Formulas for line 

A straight line’s general equation is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of a straight line equation used in geometry.

Standard form =  ax+by=c

Slope intercept form = y=mx+c

Point slope form = y-y1=m(x-x1)

Formulas for angle

1. Formula for central angle 

s=r×θ

Where, s=arc length

θ=central angle in radians 

r=length of the radius 

2. Formula for double angle – 3 formulas given below

cos θ=θ-  

sin 2θ=2sin cos  

tan 2θ=2tan 1-2

Where is, θ=angle in a right angled triangle 

How are lines and angles measured in 2d shapes

Sides, Vertices, and Angles – A 2D shape’s sides are the line segments that make up the shape. The angle between the sides is a measurement of the turn between two sides that meet at a vertex.

For example, below a square is a two-dimensional shape with four equal sides and each angle equal to 90˚.

Examine the properties of the given square PQSR to determine whether it is a 2D shape.

• All four sides are the same, PQ = QS = RS = PR.
• The PQ side is parallel to the RS side.
• The side PR is parallel to the QS.
• All four internal angles are 90 °

Conclusion

In this article we learned that, in geometry, we have horizontal, perpendicular, vertical, and parallel lines. And each line is crucial in the formation of polygons. There is no beginning or end point to the line. Lines can intersect or be perpendicular to one another. Lines are divided into two types: line segments and rays. Angles are classified as acute (90°), right equals to 90°, obtuse (>90°), and straight angle equals 180°. Angles are based on line concepts such as parallel lines, perpendicular lines, and transversal lines. Angles are divided into two types: supplementary angles and complementary angles, adjacent angles and vertically opposite angles.