Geometry (Beta) / Chapter 5: Quadrilaterals / Parallelograms

Proof: If Sides Congruent Then Parallelogram

Let's prove the following theorem:

if distance WX = distance YZ and distance WZ = distance XY, then XWZY is a parallelogram

Z W X Y

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 distance WX = distance YZ
2 distance WZ = distance XY
Proof Table
# Claim Reason
1 distance XY = distance ZW if distance WZ = distance XY, then distance XY = distance ZW
2 distance YW = distance WY distance YW = distance WY
3 △WXY ≅ △YZW if distance WX = distance YZ and distance XY = distance ZW and distance YW = distance WY, then △WXY ≅ △YZW
4 m∠XWY = m∠WYZ if △WXY ≅ △YZW, then m∠XWY = m∠WYZ
5 XW || YZ if m∠XWY = m∠WYZ, then XW || YZ
6 m∠ZWY = m∠WYX if △WXY ≅ △YZW, then m∠ZWY = m∠WYX
7 ZW || YX if m∠ZWY = m∠WYX, then ZW || YX
8 XWZY is a parallelogram if XW || YZ and ZW || YX, then XWZY is a parallelogram
Previous Lesson Next Lesson

Comments

Please log in to add comments