To prove that angle 1 is congruent to angle 4, we can use the properties of parallel lines and transversals.
Since lines k and m are parallel, and if we have a transversal that intersects both lines, various angles formed will be related based on the congruence of the angles.
Given that angle 3 is congruent to angle 4 (angle 3 ≅ angle 4), we can apply the Corresponding Angles Postulate. This postulate states that when a transversal intersects two parallel lines, the pairs of corresponding angles are congruent.
Assuming that angle 3 and angle 1 are corresponding angles created by the transversal cutting through parallel lines k and m, we can conclude that:
- Angle 1 ≅ Angle 3 (by the Corresponding Angles Postulate)
- Angle 3 ≅ Angle 4 (as given)
Now, by the Transitive Property of Congruence, since angle 1 is congruent to angle 3, and angle 3 is congruent to angle 4, we can say:
Angle 1 ≅ Angle 4
This completes the proof that angle 1 is congruent to angle 4.