Question

What is another way to summarize the outcome of this proof?

Given AX ∥ CY, 28 ∥ O9, 28 ∥ CO

a) ∠ ABX ≅ ∠ ACOY
b) ∠ AXDY ≅ ∠ GY
c) ∠ AXDY ≅ ∠ ACY
d) ∠ AXDY ≅ ∠ AOX

Answer 1

Parallel lines AX ∥ CY, 28 ∥ O9, and 28 ∥ CO imply ∠AXDY ≅ ∠ACY by Alternate Interior Angle Theorem.

c) ∠ AXDY ≅ ∠ ACY

Step-by-step explanation:

In the given scenario, we start with the information that AX is parallel to CY, 28 is parallel to O9, and 28 is parallel to CO. To determine the congruence of angles, we observe that ∠AXDY corresponds to ∠ACY. This correspondence is due to the transversal AX intersecting parallel lines CY and CO. According to the Alternate Interior Angle Theorem, when a transversal intersects two parallel lines, the alternate interior angles are congruent.

Now, let's delve into the specifics of the given options. Option (a) ∠ABX ≅ ∠ACOY is not supported by the information provided in the problem. Option (b) ∠AXDY ≅ ∠GY does not have a basis in the given parallel relationships. Option (d) ∠AXDY ≅ ∠AOX lacks support from the given parallel lines. The correct choice, option (c), ∠AXDY ≅ ∠ACY, is substantiated by the established parallel relationships, ensuring that the alternate interior angles are indeed congruent.

In conclusion, the parallel lines AX, CY, and CO lead to the congruence of ∠AXDY and ∠ACY, making option (c) the accurate summary of the proof. This aligns with the principles of geometry, specifically the Alternate Interior Angle Theorem, providing a solid foundation for the chosen answer.