A. ∠ABC ≅ ∠DBE
B. ∠BCA ≅ ∠BDE
C. ∠ACB ≅ ∠DEB
D. ∠BDE ≅ ∠ADE
E. ∠CAB ≅ ∠DAC
Answer:- The missing step in the proof is A. ∠ABC ≅ ∠DBE.
Given:
- AB is a transversal
- DE is parallel to AC
Prove:
- ∠ABC ≅ ∠DBE
| Statement | Reason |
| AB is a transversal | Definition of transversal |
| DE is parallel to AC | Given |
| ∠ABC and ∠DBE are alternate interior angles | Alternate interior angles are congruent when lines are parallel |
| ∠ABC ≅ ∠DBE | Congruence postulate |
The other answer choices are incorrect because they are not true. For example, ∠BCA is not congruent to ∠BDE because they are not corresponding angles. ∠ACB is not congruent to ∠DEB because they are not alternate interior angles. ∠BDE is not congruent to ∠ADE because they are not vertical angles. ∠CAB is not congruent to ∠DAC because they are not supplementary angles.
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