Given information
ZW is parallel to XY
ZW is congruent to XY
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What we want to prove: ZY parallel to WX
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Proof:
Statement 1: ZW is parallel to XY
Reason 1: Given
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Statement 2: ZW = XY
Reason 2: Given
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Statement 3: Angle 3 = angle 4
Reason 3: Alternate interior angle theorem
note: it might help to erase or cover up the horizontal lines of the parallelogram temporarily to help see that angles 3 and 4 are alternate interior angles.
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Statement 4: ZX = ZX
Reason 4: Reflexive property of congruence
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Statement 5: Triangle WZX = Triangle YXZ
Reason 5: SAS congruence postulate
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Statement 6: Angle 1 = Angle 2
Reason 6: CPCTC
note: CPCTC stands for "corresponding parts of congruent triangles are congruent"
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Statement 7: ZY is parallel to WX
Reason 7: Converse of alternate interior angle theorem
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This concludes the proof.
