Given line AE and line BD that intersect at point C, the following is an indirect paragraph proof proving that vertical angles ACB and ECD are congruent:

lines AE and BD intersect at point C

Assume ∠ACB and ∠ECD are not congruent. The Vertical Angles Theorem says that vertical angles must be congruent. Since this contradicts the assumption, vertical angles ACB and ECD are congruent.

Is the indirect proof logically valid? If so, why? If not, why not?
Yes. Statements are presented in a logical order using the correct theorems.
Yes. The conclusion was used to contradict the assumption.

Question

Given line AE and line BD that intersect at point C, the following is an indirect paragraph proof proving that vertical angles ACB and ECD are congruent:

lines AE and BD intersect at point C

Assume ∠ACB and ∠ECD are not congruent. The Vertical Angles Theorem says that vertical angles must be congruent. Since this contradicts the assumption, vertical angles ACB and ECD are congruent.

Is the indirect proof logically valid? If so, why? If not, why not?
Yes. Statements are presented in a logical order using the correct theorems.
Yes. The conclusion was used to contradict the assumption.