Converse of the Corresponding Angles Postulate
If two coplanar lines are intersected nu a transversla and the corresponding angles are congruent, then the lines are parallel
The Corresponding Angles Postulate states that when two parallel lines are cut by a transversal, the corresponding angles that are formed are congruent. The converse of the Corresponding Angles Postulate is also true.
Converse:
If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
In other words, if the angles that are formed by the intersection of a transversal and two lines (not parallel) are congruent, then the lines must be parallel. This is a very useful theorem in geometry, as it allows us to prove that lines are parallel without actually having to observe the angles of the lines.
To prove the converse of the Corresponding Angles Postulate, we can use a proof by contradiction. Assume that the lines are not parallel, but the corresponding angles are congruent. This means that the transversal intersects the lines at different angles. However, since the corresponding angles are congruent, there must be another transversal that intersects the lines at the same angle as the first transversal. This second transversal would create a new set of corresponding angles that are congruent, but this time the lines are parallel. This contradiction proves that the original assumption must be false, and thus the converse of the Corresponding Angles Postulate must be true.
More Answers:
Locating The Center Of A Circle: Methods And Equations For Coordinate Determination.The Properties Of Circles: Circumference, Area, Chord, Tangent, Secant, And Arcs
Converse Of The Alternate Interior Angles Theorem: Two Lines Are Parallel If Alternate Interior Angles Are Congruent.