UPSKILL MATH PLUS

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Learn more### Theory:

Geometry derives from the Greek word 'earth measurement', which is the mathematics branch concerned with the properties and relationships of points , lines, surfaces, solids, and analogs of higher dimensions.

A specific position or location on the surface of the plane is referred to as a point.

The above figure shows point \(A\) and \(B\).

A point is sort of an invisible dot that may determine a location/position but can't be extended. To represent the location/position, we label each point using an English alphabet.

Example:

We are planning to locate the five-place (let them be \(A\), \(B\), \(C\), \(D\) and \(E\)) on a map using the concept of points and label them accordingly.

When a line is drawn between the two points, it is referred to as a line segment.

The above figure shows a line segment \(AB\) and is represented as $\overline{\mathit{PQ}}$.

A line segment is used to determine the distance between two points.

Example:

We are planning to demonstrate the distance between the five places (let them be \(A\), \(B\), \(C\), \(D\) and \(E\)) on a map using the concept of a line segment and label them accordingly. Here the distance between \(A\) and \(B\) is shown by drawing a line between \(A\) and \(B\). Similarly, the distance between \(B\) and \(E\), and the distance between \(C\) and \(D\) are shown in the following picture.

A line may be a combination of points that extends infinitely in both directions. A line is labelled sort of a line segment with a bidirectional arrow over the label.

The above figure shows a line \(AB\) and is represented as $\overleftrightarrow{\mathit{AB}}$ or $\overleftrightarrow{\mathit{BA}}$.

Example:

\(100\) metres track is to illustrate the concept of the line. A track may be a line that extends infinitely in both the direction without having a fixed starting and ending point.

When three or more points lie on the same line are called collinear points.

The above figure shows the collinear points \(A\), \(B\) and \(C\). These points are collinear points because all three points lie on the same line.

Example:

Arrange the more number of cups to validate the concept of the collinear points.

A ray is often defined as a straight line that starts from a point and extends indefinitely in one direction.

The starting point that's fixed at one end is termed as a vertex of a ray. Ray is additionally one-dimensional entity as we will move endlessly in one direction alone.

The above figure shows a ray \(AB\) and is represented as $\underset{\mathit{AB}}{\u27f6}$.

Example:

We have a battery-operated torch on one end of the road and light from the torch (called as a line segment) is travelling in a straight line towards the other direction. Since we don't know the end of that light, we will say that this line segment from a fixed source may be a ray.