Angle EBC equals angle BCA due to the Alternate Interior Angles Theorem, as lines AC and DE are parallel with BC as the transversal, confirming their congruence.
In the given diagram it can be proven that Angle EBC is equal to angle BCA because these are alternate interior angles, as we can see that the two lines AC and DE are parallel with BC as the transversal."
This statement suggests that you are using the Alternate Interior Angles Theorem, which states that if two parallel lines are intersected by a transversal, then the pairs of alternate interior angles are congruent.
In the given case:
- Lines AC and DE are parallel.
- Line BC acts as the transversal.
Therefore, according to the Alternate Interior Angles Theorem, angle EBC and angle BCA would be congruent. This is a common geometric argument used when dealing with parallel lines and transversals.