Statements Reasons

Question

1. Quadrilateral ABCD, AD¯¯¯¯¯¯¯¯ ⊥ CD¯¯¯¯¯¯¯¯, BC¯¯¯¯¯¯¯¯ ⊥ CD¯¯¯¯¯¯¯¯ 1. given
2. ∠C and ∠CDE are right angles

2. Perpendicular lines form right angles.
3. ∠C ≅ ∠CDE 3. All right angles are congruent.
4. ? 4. Converse of Alternate Interior Angles Theorem
5. ABCD is a trapezoid 5. definition of a trapezoid (A quadrilateral with exactly one pair of opposite parallel sides).


Which statement best completes the step 4 of the proof?

(1 point)
Responses

AD¯¯¯¯¯¯¯¯ ∥ AB¯¯¯¯¯¯¯¯AD¯¯¯¯¯¯¯¯ ∥ AB¯¯¯¯¯¯¯¯

AD¯¯¯¯¯¯¯¯ ∥ CD¯¯¯¯¯¯¯¯AD¯¯¯¯¯¯¯¯ ∥ CD¯¯¯¯¯¯¯¯

AD¯¯¯¯¯¯¯¯ ∥ BC¯¯¯¯¯¯¯¯

Answer 1

The statement that best completes step 4 of the proof is:

AD¯¯¯¯¯¯¯¯ ∥ BC¯¯¯¯¯¯¯¯

This is justified by the Converse of the Alternate Interior Angles Theorem, which states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. In this case, since ∠C and ∠CDE are right angles, and ∠C ≅ ∠CDE, it follows that the lines AD and BC are parallel.