Given the figure with L1 / / L2 and T1 // T2. Prove that ∠x ≅ ∠y. Kindly use Two-column proof.

Question

Answer 1

Note that L1 is a transversal of parallel lines T1 and T2, and T2 is a transversal of parallel lines L1 and L2. We can use what we know about corresponding and vertical angles, along with the transitivity of congruence, to complete the proof:

1. ∠x ≅ ∠1 (These are corresponding angles).
2. ∠1 ≅ ∠2 (These are vertical angles).
3. ∠2 ≅ ∠y (These are corresponding angles).
4. ∠1 ≅ ∠y (By lines 2 and 3, and the transitivity of angle congruence).
5. ∠x ≅ ∠y (By lines 1 and 4 and the transitivity of angle congruence).