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Understanding angles

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Understanding angles

Maths

2021-08-10 14:07:46

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Understanding angles

In geometry, we come across many words, Transversal Is among them. We can define transversal as a line that passes through the two lines in the same plane at two distinct points. If you want to understand detail about the parallel lines you have to know the meaning of transversal. It plays an important role in establishing the parallelism of two or more other straight lines in a plane. 

 Definition of Transversal 

A transversal is a line that intersects two straight lines into different points. For example, if we say there are two lines. Line X  and line Y are the two parallel lines or non-parallel lines and line Z passes through both the lines at two distinct points. Then, line Z is known as the transversal of line X and line Y.

Properties of transversal

A Transversal is a line that intersects two lines at distinct points. These lines can be parallel or non-parallel lines.

It cuts the two lines.

Several angles can be formed by using transversal.

The total of interior angles which are Formed by transversal is  180°.

Each pair of alternate angles which are formed by a transversal are the same.

Each pair of corresponding angles which are formed by a transversal are the same.

Each pair of interior angles on the same stopicIde, which are formed by a transversal, are supplementary angles.

Transversals do not have any symbols in maths. 

Angles forming by using transversal ( parallel lines)

When a transversal cuts two lines that are parallel to each other, then several angles are formed by these two intersections. Those are called angles formed due to transversal. The following are the angles that are formed using transversal

Corresponding Angles

Interior angles

Alternate angles

Exterior angles

Let us go through all the angles one by one:

Corresponding angles: Any pair of angles, each of which is on the same stopicIde of one of two lines cut by a transversal and on the same stopicIde of the transversal are known as corresponding angles. 

Interior angles: Interior angles are the angles that lie instopicIde and on the same stopicIde of the transversal. The total interior angle is 180° ( supplementary angles).

Alternate angles: Alternate angles are angles that occur on the opposite stopicIde of the transversal line. They have the same size. It looks like the letter  Z. The two types of alternate angles are alternate interior and alternate exterior angles. If angles are formed instopicIde the interior part of a transversal, they are known as alternate interior angles. If angles are formed outstopicIde or on the exterior part of a transversal, it is known as exterior alternate angles. 

Exterior angles: Angles that are formed on the exterior stopicIde of the outer corners of the transversal are known as exterior angles. The total of the exterior angle is also 180°.

Angles formed by a transversal (  non-parallel lines)

When there are non-parallel lines and a transversal is drawn,  The exterior angles still add up to a constant angle, but the total will not be 180°.

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