Geometry: Angles Formed by Parallel Lines and a Transversal

Geometry: Angles Formed by Parallel Lines and a Transversal

Geometry: Angles Formed by Parallel Lines and a Transversal 150 150 SchoolTutoring Academy

A transversal is a line that intersects two or more lines. When a transversal cuts (or intersects) parallel lines several pairs of congruent (equal) and supplementary angles (sum 180°) are formed.

 

 

In the above figure transversal t cuts the parallel lines m and n.

Following types of congruent angles are formed:

Corresponding angles: these angles are located on the same side of the transversal. In the above figure 1 and 5, 2 and 6, 3 and 7, 4 and 8 are pairs of corresponding angles.

Alternate Interior angles: These angles are found between the parallel lines on the alternating sides of the transversal. Notice the Z (marked in red and green) on the diagram. These angles are in the corners of the Z. In the above figure 3 and 6, 4 and 5 form the pairs of alternate interior angles.

Alternate Exterior angles: These angles are found outside the parallel lines on the alternating sides of the transversal. 1 and 8, 2 and 7 are the pairs of alternate exterior angles.

Supplementary angles are formed on the same side of the transversal in between the parallel lines. 3 and 5, 4 and 6 are supplementary angles.

 

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