Corresponding Angles

The word “corresponding” implies that the angles can be comparable or in equivalent (congruent). Surprisingly, the transversal that meets two parallel lines forms equivalent angles that are congruent. The corresponding angles are not equivalent when the transversal connects two non-parallel lines. When two lines are crossed by another line in plane geometry, corresponding angles are formed. The equivalent angles are the angles formed by matching corners at each junction. In other terms, a comparable angle is one that maintains the same correlative location as another angle in the figure at the same time. Corresponding angles are a form of angle pair that is quite similar to one another. You can have alternate internal angles and alternate external angles as matching angles.

Definition of corresponding angles

“In geometry, matching angles are created when an intersecting transversal line crosses over two straight lines. Corresponding angles are angles that are positioned in the same relative location on distinct intersections.”

• The first and second lines are parallel. As a result, we have two lines that are parallel.

• Lines 1 and 2 cross at the intersection of line 3. As a result, parallel lines have been intersected.

• Angles 1 and 2 are shown in the diagram to be in the same relative position – the upper right side angles in the junction region.

Figure 1: corresponding angles

When two rays, each with one terminus, intersect at one point, they produce an angle. A vertex is the point where two rays intersect. The angle is measured by the distance between the two beams. Angles are frequently referred to in geometry using the symbol.

Angles, transversal lines, and parallel lines are only a few of the elements.

Transversal line: A transversal line is a line that connects two other lines by crossing or passing through them. The transversal goes through both lines at the same angle when the two other lines are parallel. The two other lines, on the other hand, do not have to be parallel for a transversal to cross them, as seen here:

Straight line: A straight line, also known as a flat angle, creates a straight angle. This angle is 180 degrees in length. Two or more angles that add up to 180 °  can also constitute a straight angle.

Parallel lines: On a two-dimensional plane, parallel lines are two lines that never meet or cross. There are particular properties concerning the angles created when a transversal crosses between parallel lines that do not occur when the lines are not parallel. Lines m and n have arrows pointing to the left. Lines m and n are parallel, as indicated by these arrows.

There are different kinds of corresponding angles

1. Corresponding angles created by parallel lines and transversals.

2. Corresponding angles created by Non-parallel lines and transversals

Theorem of Corresponding Angles

According to the Corresponding Angles Theorem,

• When a transversal cuts two parallel lines, the pairs of corresponding angles are congruent.

• A theorem is a proven assertion or a widely held belief that has been demonstrated to be correct. This theorem’s inverse, which is essentially the reverse, is likewise a proven statement:

• The lines are parallel if a transversal cuts two lines and the accompanying angles are equivalent.

These theorems can be used to solve geometry difficulties and identify missing data.

How to find to Find Corresponding Angles?

Drawing the letter F on the accompanying figure is one method of determining matching angles. Make the letter face whichever way you like and match the angles.

Example 1: Find the missing angles in the diagram below with ∠d=30° 

 Figure 2

∠d=30° 

∠d=∠b ……..Vertically opposite angles

∠b=30° 

∠b=∠g=30° Corresponding angles

∠d=∠f Corresponding angles

∠f=30° 

∠b+∠a=180° Supplementary angles

∠a+30°=180° 

∠a=150° 

∠a=∠e= Corresponding angles

∠e=150° 

∠d=∠h=30° ………Corresponding angles

Example 2: A figure’s two matching angles are 9x + 10 and 55. Calculate the value of x.

9x+10 And 55.

Solution:

The two angles that correspond to one other are always congruent.

9x+10=55 

9x=55-10 

9x=45 

x=5 

Corresponding Angles Application

There are numerous applications of corresponding angles.

• Window grills are usually horizontal and vertical, forming several squares. The matching angles are formed by each vertex of the square.

• The pillars support the bridge. All of the pillars are connected in such a way that the angles of the corresponding pillars are the same.

• The railway tracks are constructed in such a way that all of the corresponding angles on the track are equal.

Conclusion

In this article we learn, The word “corresponding” implies that the angles can be comparable or in equivalent (congruent). Surprisingly, the transversal that meets two parallel lines forms equivalent angles that are congruent. The corresponding angles are not equivalent when the transversal connects two non-parallel lines. When a transversal travels over two lines, it creates corresponding angles. The Corresponding Angles Theorem says that if a transversal cuts two parallel lines, the corresponding angles are congruent.