Question

Given line m is not parallel to line n, prove ∠3 is not congruent to ∠5 by contradiction.

Answer 1

∠3 is congruent to ∠5 must be false, and we can conclude that ∠3 is not congruent to ∠5.

Explanation:

To prove that ∠3 is not congruent to ∠5 by contradiction, we assume that ∠3 is congruent to ∠5. Since line m is not parallel to line n, we know that ∠3 and ∠5 are corresponding angles. If ∠3 is congruent to ∠5, then lines m and n must be parallel by the Corresponding Angles Postulate. This contradicts the given statement that line m is not parallel to line n. Therefore, our assumption that ∠3 is congruent to ∠5 must be false, and we can conclude that ∠3 is not congruent to ∠5.

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