Question

complete the missing statements/reasons in the proof. given: ; ∠bac ≅ ∠dec prove: ∠abc ≅ ∠edc image of triangle diagram accessible description statements and reasons statements reasons blank given ∠bac ≅ ∠dec given ∠acb ≅ ∠ecd 1. △abc ≅ △edc asa postulate ∠abc ≅ ∠edc 2. 1. vertical angles theorem; 2. reflexive property 1. reflexive property; 2. substitution property 1. vertical angles theorem; 2. cpctc 1. corresponding angles theorem; 2. cpctc

Explanation:

To solve this, we analyze each step:

1. For \( \angle ACB \cong \angle ECD \), these are vertical angles (formed by intersecting lines), so the Vertical Angles Theorem applies.
2. After proving \( \triangle ABC \cong \triangle EDC \) by ASA, \( \angle ABC \cong \angle EDC \) follows because corresponding parts of congruent triangles are congruent (CPCTC).

Answer:

1. Vertical Angles Theorem; 2. CPCTC