Line PQ and line RS are parallel. Line XY is perpendicular to line PQ at point A. Prove that line XY is perpendicular to line RS.
Given:
Line PQ is parallel to line RS. Line XY is perpendicular to line PQ at point A. To Prove:
Line XY is perpendicular to line RS.
Proof: Assume, for the sake of contradiction, that line XY is not perpendicular to line RS. Since line XY is perpendicular to line PQ at point A, angle XAB is a right angle (90 degrees). Now, since line PQ is parallel to line RS, angle XAB and angle XBA are corresponding angles. According to the Corresponding Angles Theorem, when a transversal intersects two parallel lines, corresponding angles are congruent. Therefore, angle XBA is also a right angle (90 degrees), as angle XAB is a right angle. However, if both angle XAB and angle XBA are right angles, then line XY must be perpendicular to line RS. This contradicts our assumption that line XY is not perpendicular to line RS. Hence, our assumption is false, and line XY must be perpendicular to line RS.
Therefore, it has been proven that if line PQ is parallel to line RS, and line XY is perpendicular to line PQ at point A, then line XY is perpendicular to line RS.
Can someone draw the same based on the given statement i wont show mine