A transversal is a straight line that crosses two or more straight lines. In this lesson, we will focus on transversals that cross two or more parallel lines.
When a line (called a transversal) intersects a pair of parallel lines, corresponding angles are formed. Corresponding angles are angles that are in the same relative position at an intersection of a transversal and at least two lines. If the two lines are parallel then the corresponding angles are congruent.
One way to find the corresponding angles is to draw a letter F on the diagram. The letter F can also be facing the other way.
In the above diagram, d and h are corresponding angles.
The other corresponding pairs of angles in the above diagram are:
b and f ; c and g ; a and e.
(Corresponding angles found in a F-shaped figure)
In the following diagram, all the lines shown are straight lines. Line m is parallel to line n. List a pair of corresponding angle.
d and h are corresponding angles.
The Corresponding Angle Postulate states that
When a transversal intersects two parallel lines, the corresponding angles are equal.
A postulate does not need to be proved, but is assumed to be self-evident and true.The following video explains more about corresponding angles:
The converse of the corresponding angle postulate states that
How to use the converse of corresponding angles postulate to prove lines are parallel?
If two lines and a transversal form corresponding angles that are congruent then the two lines are parallel.
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