Proof: If Parallelogram Diagonal Then Congruent Triangles

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	WX || ZY	if WXYZ is a parallelogram, then WX || ZY (Parallelogram Property 2)
2	WZ || XY	if WXYZ is a parallelogram, then WZ || XY (Parallelogram Property 3)
3	m∠XWY = m∠WYZ	if WX || ZY, then m∠XWY = m∠WYZ (Alternate Interior Angles Theorem (Converse) 6)
4	m∠WYZ = m∠YWX	if m∠XWY = m∠WYZ, then m∠WYZ = m∠YWX (Angle Symmetry 4)
5	m∠ZWY = m∠WYX	if WZ || XY, then m∠ZWY = m∠WYX (Alternate Interior Angles Theorem (Converse) 6)
6	m∠ZWY = m∠XYW	if m∠ZWY = m∠WYX, then m∠ZWY = m∠XYW (Angle Symmetry Example)
7	distance WY = distance YW	distance WY = distance YW (Distance Equality Property)
8	△ZWY ≅ △XYW	if m∠ZWY = m∠XYW and distance WY = distance YW and m∠WYZ = m∠YWX, then △ZWY ≅ △XYW (ASA Property)

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