Proof: Quadrilateral Parallel

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	m∠XYW = m∠ZWY	if XY || WZ, then m∠XYW = m∠ZWY (Alternate Interior Angles Theorem (Converse) 3)
2	distance YW = distance WY	distance YW = distance WY (Distance Equality Property)
3	△XYW ≅ △ZWY	if distance XY = distance ZW and m∠XYW = m∠ZWY and distance YW = distance WY, then △XYW ≅ △ZWY (SAS Property)
4	m∠YWX = m∠WYZ	if △XYW ≅ △ZWY, then m∠YWX = m∠WYZ (Congruent Triangles Property 6)
5	m∠XWY = m∠WYZ	if m∠YWX = m∠WYZ, then m∠XWY = m∠WYZ (Angle Symmetry B)
6	XW || YZ	if m∠XWY = m∠WYZ, then XW || YZ (Alternate Interior Angles Theorem 4)

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