HELP ME WITH TEST QUESTION
prove the Converse of the Alternate Exterior Angle Theorem using the figure. Given: the figure; 1 is congruent to 8 Prove: m is parallel to n
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To prove the Converse of the Alternate Exterior Angle Theorem, we need to show that if two lines are intersected by a transversal and the exterior alternate angles are congruent, then the lines are parallel.
Given:
- We have a figure with two lines, m and n, intersected by a transversal.
- We are given that angle 1 is congruent to angle 8.
To prove that lines m and n are parallel, we can use a proof by contradiction method. We assume that lines m and n are not parallel and work towards a contradiction.
Proof by Contradiction:
1. Assume that lines m and n are not parallel.
2. When a transversal intersects two lines, alternate exterior angles are congruent if and only if the lines are parallel. Therefore, if angle 1 is congruent to angle 8, lines m and n must be parallel.
3. This contradicts our assumption in step 1 that lines m and n are not parallel.
4. Thus, our assumption was incorrect, and lines m and n must be parallel.
Therefore, we have proven the Converse of the Alternate Exterior Angle Theorem using the information given in the figure.