Question

Given: ef∥gh and ab∥cd. Prove: ∠gji ≅∠lkf.

Answer 1

Using the properties of parallel lines and angles, we can prove that ∠gji ≅∠lkf.

Step-by-step explanation:

Given that ef∣gh and ab∣cd, we can use the properties of parallel lines and transversals to prove that ∠gji ≅∠lkf.

1. Since ef∣gh, the alternate interior angles ∠gji and ∠ghf are congruent.
2. Similarly, since ab∣cd, the alternate interior angles ∠lkf and ∠lke are congruent.
3. Using the transitive property of congruence, we can conclude that ∠gji ≅∠ghf ≅∠lkf.