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Given line m is not parallel to line n, prove ∠4 is not congruent to ∠6 by contradiction. (2 points for the assumption statement, 4 points for the remainder of the proof)

Given line m is not parallel to line n, prove ∠4 is not congruent to ∠6 by contradiction-example-1
User KhAn SaAb
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Assumption: Let's assume that ∠4 is congruent to ∠6.

Proof by contradiction:

1. If ∠4 is congruent to ∠6, it implies that corresponding angles formed by line m and line n are congruent due to the transversal property.

2. Let's consider ∠1 and ∠5, which are corresponding angles formed by line m and line n.

3. If ∠4 is congruent to ∠6, it would mean that ∠1 is congruent to ∠5 as well.

4. However, this contradicts the given statement that line m is not parallel to line n. When a transversal intersects two lines, the corresponding angles are congruent only if the lines are parallel.

5. Since line m is not parallel to line n, ∠1 cannot be congruent to ∠5.

6. Therefore, our assumption that ∠4 is congruent to ∠6 leads to a contradiction.

By the contradiction, we can conclude that ∠4 is not congruent to ∠6.

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User Akshay Shrivastav
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