November 24, 2022

Corresponding Angles

The angles that are formed if two parallel lines get intersected by the transversal are known as corresponding angles. Opening-closing of a tiffin box, parallel railway tracks, etc. are some of the examples of corresponding angles. Those are created in the corresponding corners with the transversal.

What are Corresponding Angles?

According to the definition of corresponding angles, if a line intersects two parallel lines, the angles that are formed at each of the intersections are called corresponding angles to each other.

Let us take an example:

  • Line 1 and Line 2 are two parallel lines, and line 3 intersects the two lines.
  • As per geometry, line 1 and line 2 are parallel to each other. Therefore, we get two parallel lines.
  • Line 3 is the intersection of the two parallel lines 1 and 2. Hence, we get the intersecting line and intersected parallel lines.

If we picture the figure, then we can see that the angles formed by the intersection are of equal relative position.

Therefore, by this example, we are successful in justifying the definition of corresponding angles. Hence, two angles that are formed are called corresponding angles.

We can figure out if any two angles are corresponding or not by looking at the diagram. Also, the angles that are formed by the third line that is intersecting two parallel lines are the same angles that are congruent to each other. On the other hand, if the third line or the transversal intersects two lines that are not parallel to each other, then the corresponding angles are not congruent.

Corresponding Angles Theorems

In terms of the corresponding angles theorems, we know that when a line intersects two parallel lines, then the two corresponding angles formed at the intersections are congruent.

Converse of Corresponding Angles Theorem

The converse theorem of corresponding angles states that when the corresponding angles formed at the intersections of the lines are congruent, then the two lines are said to be parallel to each other.

If a transversal cuts two lines and the corresponding angles formed at the intersections are of equal measure, then the two intersected lines by the transversal are said to be parallel to each other. This is what the converse of corresponding angles theorem states.

Important Points 

If a line intersects two parallel lines, then the angles formed at the intersections are known as corresponding angles to each other.

  • The corresponding angles are congruent as well.
  • When the corresponding angles formed at the intersectional regions are congruent, then two intersected lines are parallel to each other.

What are Angles?

In the terms of geometry, if two rays or straight lines join at their endpoints, then an angle is formed. The rays or lines are called the arms or sides of the formed angle. There are a variety of angles.

Types of Angles

Let us know about the 6 different types of angles. Every angle has its own identity based on the measurement.

  • Acute angle- If an angle measures greater than 0 degrees and less than 90 degrees, then it is known as an acute angle.
  • Obtuse angle- If an angle measures greater than 90 degrees but less than 180 degrees, then it is called an obtuse angle.
  • Reflex angle- If an angle measures greater than 180 degrees and less than 360 degrees, it is known as a reflex angle.
  • Straight angle- If the angle is equal to 180 degrees, it is called the straight angle.
  • Complete angle- If the measurement of an angle is equal to 360 degrees, it is known as a complete angle.

To know more about corresponding angles, visit Cuemath and book free sessions.

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