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# Possible reasons to proving the validity of the construction: -The line through point Q is perpendicular to PS -The point Q is on the line through PS and the line through PS is perpendicular to the

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Question: Once the construction below is complete, creating a parallel line to PS through point Q which of the reasons listed contribute to proving the validity of the construction?

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To provide a relevant response, it is important to have a visual representation or a list of steps in the construction, as well as the specific reasons listed that are under consideration for proving the validity of the construction once the parallel line through point Q is created. Assuming you are using basic Euclidian geometry, the most common method for constructing a parallel line through point Q would be as follows: 1. Draw a line segment PS and a distinct point Q not on the line. 2. Draw a circle centered at Q that intersects PS at points A and B. 3. Draw a circle centered at A with the same radius as the circle from step 2. 4. Draw a circle centered at B with the same radius as the circle from step 2. 5. The intersection point of the circles from steps 3 and 4 is point R. 6. Draw a line QR which will be parallel to PS. For this construction, the reasons contributing to proving the validity of the construction are: 1. Corresponding angles, formed by the transversal QR and the lines AR and BS, are congruent. 2. The Alternate Interior Angle Theorem, which states that if a transversal intersects two parallel lines, then the alternate interior angles are congruent. 3. The Converse Alternate Interior Angle Theorem, which states that if a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel. 4. Eucledian axioms, such as those involving circles, parallels, and congruence. With a thorough understanding of the construction process and analysis of the reasons listed, you can identify which of the reasons listed contribute to the validity of the construction once the parallel line through point Q has been created.

June 21, 2023, 11:06 a.m.

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