If two parallel lines are cut by a transversal so the alternate interior anglesare congruent, then the lines are parallel.
The point where two lines meet is known as an angle
For two parallel lines that are transversal, some of the angles are equal i.e. they are congruent to each other.
We can have the following as shown in the figure;
- corresponding angles
- vertically opposite angles
- alternate interior and exterior angles
Hence we can conclude that if two parallel lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
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