Mathematics, 22.10.2020 20:01 shadekashakay

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.

Lines a and c intersect at point S. Line c is diagonal and also contains points R, Q, P. Line a is horizontal and also contains points U, T.

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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