zw is parallel as yzzw is congruent to myprove zy is parallel to wx​

Accepted Solution

Given informationZW is parallel to XYZW is congruent to XY---------------------What we want to prove: ZY parallel to WX==============================================Proof:Statement 1: ZW is parallel to XYReason 1: Given--------------------Statement 2: ZW = XYReason 2: Given--------------------Statement 3: Angle 3 = angle 4Reason 3: Alternate interior angle theoremnote: 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.--------------------Statement 4: ZX = ZXReason 4: Reflexive property of congruence--------------------Statement 5: Triangle WZX = Triangle YXZReason 5: SAS congruence postulate--------------------Statement 6: Angle 1 = Angle 2Reason 6: CPCTC note: CPCTC stands for "corresponding parts of congruent triangles are congruent"--------------------Statement 7: ZY is parallel to WXReason 7: Converse of alternate interior angle theorem--------------------This concludes the proof.