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If PQRS is a parallelogram, then the following statement holds true.
PQ≅SR and QR≅PS
This can be proven using the ASA Congruence Theorem. In the parallelogram PQRS, the diagonal QS is drawn.
According to the definition of a parallelogram, the opposite sides are parallel, PQ∥SR and QR∥PS.
This can be summarized by a two-column proof.
0. Statement
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0. Reason
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1. PQRS is a parallelogram.
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1. Given
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2. Draw the diagonal QS.
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2. Diagonal to create triangles.
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3. PQ∥SR, QR∥PS
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3. Parallel lines
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4. ∠PQS≅∠QSR, ∠PSQ≅∠RQS
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4. Alternative Angle Theorem
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5. △PQS≅△RSQ
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5. ASA Congruence Theorem
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6. PQ≅SR, QR≅PS
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6. Parallel lines in a parallelogram are congruent.
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