In the scenario of parallel lines AB and CD intersected by transversal MN at points E and F, angle BEF is congruent to angle EFC due to the corresponding angles postulate.
When two parallel lines, AB and CD, are intersected by a transversal line MN at points E and F, certain angle relationships emerge. According to the corresponding angles postulate, angle BEF is congruent to angle EFC. This postulate states that when a transversal intersects two parallel lines, the pairs of corresponding angles formed are equal.
To elaborate, the parallel lines create a set of corresponding angles on each side of the transversal. In this case, angle BEF and angle EFC are positioned on the same side of line MN and on the same side of the parallel lines. As a result, these angles are congruent.
The reason behind this congruence lies in the nature of parallel lines. Since AB and CD are parallel, the corresponding angles formed by the transversal are equal. Consequently, angle BEF and angle EFC share the same measure, establishing an angle relationship of congruence.
In summary, when a transversal intersects two parallel lines AB and CD, the corresponding angles BEF and EFC are congruent, adhering to the corresponding angles postulate.