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Notes on Transversals

 

Transversal:  is a line that intersects two or more lines in a plane at different points.  When the lines that are intersected are parallel the angles that are formed are related.

                                      In this figure there are a set of parallel lines, m and n and                                  a transversal line l. 

 

 

 

 

Interior Angles: The interior angles are all the angles that are inside the parallel lines.  In the above figure <2, <6, <3 and <7 are interior angles.

Alternate interior angles are pairs of angles that are inside the parallel lines and are diagonally on the opposite side of the transversal.  In the above figure there are two sets of alternate interior angles.  Angles <2 and <7 are alternate interior angles and <6 and <3 are alternate interior angles.

When a transversal intersects a pair of parallel lines, Alternate interior angles have the same measure.

 

Exterior Angles: The interior angles are all the angles that are outside the parallel lines.  In the above figure <1, <5, <4 and <8 are interior angles.

Alternate exterior angles are pairs of angles that are outside the parallel lines and are diagonally on the opposite side of the transversal.  In the above figure there are two sets of alternate exterior angles.  Angles <1 and <8 are alternate interior angles and <5 and <4 are alternate exterior angles.

When a transversal intersects a pair of parallel lines, Alternate exterior angles have the same measure.

 

Corresponding angles: are pairs of angles that are in the same position relative to the transversal.  In the above diagram there are four sets of corresponding angles. <1 and <3; <2 and <4; <5 and <7; <6 and <8.

When a transversal intersects a pair of parallel lines, Corresponding angles have the same measure

 

Vertical angles: are pairs of angles that are formed by intersecting lines. In the above figure there are four sets of vertical angles. <1 and < 6; <2 and <5, <3 and <8, <4 and <7 are sets of vertical angles.

Vertical angles are always congruent (the same measure).