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For two or more lines, a transversal is any straight line that intersects two lines at distinct points. In the following figure, L1 and L2 are two lines that are cut at A and B by a transversal L0, resulting in a number of angles being formed. We observe that there are 8 angles formed.
There is a specific terminology associated with the angles formed when a transversal cuts two lines, as shown above. When two lines are intersected by a transversal, 8 angles are formed. Among these,
These angles are classified into the following types based on their positions.
Corresponding AnglesWhen a transversal cuts two other lines, corresponding angles are the angles that occupy the same relative positions. Corresponding angles are on the same side of the transversal. The following pairs of angles are the corresponding angles:
Alternate Interior AnglesAngles with different vertices, lying on the alternate sides of the transversal, and interior to the lines are called alternate-interior angles. Among the 4 interior angles, we find 2 pairs of angles that lie on the alternate sides of the transversals, having different vertices.The following pairs of angles are alternate interior angles: Alternate Exterior AnglesAngles with different vertices, lying on the alternate sides of the transversal, and exterior to the lines are called alternate exterior angles. Among the 4 exterior angles, we find 2 pairs of angles that lie on the alternate sides of the transversals. The following pairs of alternate exterior angles are : Co-interior AnglesAngles with different vertices, lying on the same sides of the transversal, are called co-interior angles. The following pairs of angles are co-interior angles or same-side interior angles: We will now go on to the specific case of two parallel lines being cut by a transversal. The following are the properties of the 8 angles so formed.
Related topics on Transversals and Related Angles
Important Notes:
How to Find if Lines Parallel or Not
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Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles. These are formed in the matching corners or corresponding corners with the transversal. What are Corresponding Angles?The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other. According to geometry, and the definition of the corresponding angles, we can say that:
Hence, our corresponding angles definition seems to be justified. Therefore, we can say that angles 1 and 2 are corresponding angles. Now that we have understood the definition of corresponding angles, we can figure out whether any two given angles are corresponding or not in any given diagram. The word “corresponding” itself suggests that the angles can be either inequivalent or equivalent (congruent). Surprisingly, corresponding angles formed by the transversal that intersects two parallel lines are angles that are congruent. When the transversal intersects two non-parallel lines, the corresponding angles are not congruent. How to Find Corresponding Angles?We know that each intersection point has 4 angles. Now, each of the four angles in the first intersection region will have another one with the same relative position in the second intersection region. Now, we will separate each of these four angles into different categories. Look at the table below to get a better understanding of the different types of corresponding angles.
Corresponding Angles TheoremAccording to the corresponding angles theorem, the statement “If a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent” is true either way. The Converse of Corresponding Angles TheoremThe corresponding angles converse theorem would be, “If the corresponding angles in the two intersection regions are congruent, then the two lines are said to be parallel. What if a transversal intersects two parallel lines and the pair of corresponding angles are also equal? Then, the two lines intersected by the transversal are said to be parallel. This is the converse of the corresponding angle theorem. Important Notes on Corresponding Angles
Challenging Question on Corresponding Angles The following information has been given regarding angles A, B, C, and D :
Find the angle (other than B), which will be congruent to angle A.
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FAQs on Corresponding AnglesCorresponding angles in geometry are defined as the angles which are formed at corresponding corners with the transversal. When the two parallel lines are intersected by the transversal it forms the pair of corresponding angles. ☛ To know more about corresponding angles check now:
What are the Two Types of Corresponding Angles?According to the definition of the corresponding angles, we can classify corresponding angles further into two types listed below:
☛ Check Corresponding Angles Worksheets now for more practice. Do Corresponding Angles Add Up to 180?Yes, corresponding angles can add up to 180. In some cases when both angles are 90 degrees each, the sum will be 180 degrees. These angles are known as supplementary corresponding angles. ☛ Check Supplementary angles now for more clarification. What are Alternate and Corresponding Angles?Alternate angles are angles that are at relatively opposite positions to each other; while the corresponding angles are the angles that are at relatively same positions to each other. Can Corresponding Angles be Consecutive Interior Angles?No corresponding angles can not be considered as consecutive interior angles because the consecutive interior angles are the angles that are on the same side of the transversal but inside the two parallel lines. Can Corresponding Angles be Right Angles?If the transversal is perpendicular to the given parallel lines, then the corresponding angles of a transversal across parallel lines are right angles, all angles are right angles. ☛ Check Supplementary angles now for better understanding. What do Corresponding Angles Look Like?When two parallel lines are intersected by a transversal, the angles so formed occupying the same relative position at each intersection are corresponding angles. When two parallel lines are crossed by a transversal, then the angles in the same corners of each line are said to be corresponding angles and the transversal will look like a straight line. What do you Understand by Corresponding Angles Postulate?According to the corresponding angles postulate, the corresponding angles are congruent if the transversal intersects two parallel lines. What is the Converse of Corresponding Angles Postulate?We just read that the corresponding angles postulate states that the corresponding angles are congruent if the transversal intersects two parallel lines. Whereas converse of corresponding angles postulates says, if the corresponding angles in the two intersection regions are congruent, then the two lines are said to be parallel. Are Corresponding Angles Sum up to 90 Degrees?If the corresponding angles are equal then in some cases when both angles are 45 degrees each, the sum will be 90 degrees. These angles are known as complementary corresponding angles. ☛ Check complementary angles now for more details. |