student74929
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Determine the missing information in the paragraph proof. Given: Lines a and c intersect at point S, creating 4 angles. Prove: Corresponding angles are congruent. We are given that lines a and c intersect at point S. Translate line a down line c until point S reaches point Q. Call the new line through Q line b. Because translations preserve orientation, lines a and b are ________. Because translations preserve angle measure, ∠RSU ≅ ∠RQU'. For the same reason, ∠RST ≅ ∠RQT', ∠PSU ≅ ∠PQU', and ∠PST ≅ ∠PQT'. Each of the angle pairs are corresponding angles. Therefore, corresponding angles are congruent. parallel perpendicular congruent reflected

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The test i took said the answer was Parallel
JeanaShupp

Answer: Parallel.

Step-by-step explanation:

Given: Lines a and c intersect at point S, creating 4 angles.

To Prove: Corresponding angles are congruent.

We are given that lines a and c intersect at point S.

Translate line a down line c until point S reaches point Q.

Call the new line through Q line b.

We know that translations preserve orientation then every point on line b is equidistant from every points on line a.

Therefore,  lines a and b are parallel by the definition of parallel lines.

Hence, the complete statement is Because translations preserve orientation, lines a and b are parallel.