Proof: If Diagonals Congruent Then Rectangle

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	distance ZW = distance YX	if WXYZ is a parallelogram, then distance ZW = distance YX (If Parallelogram Then Sides Congruent 2)
2	distance WX = distance XW	distance WX = distance XW (Distance Equality Property)
3	distance XZ = distance WY	if distance WY = distance XZ, then distance XZ = distance WY (Symmetric Property of Equality)
4	△WXZ ≅ △XWY	if distance WX = distance XW and distance XZ = distance WY and distance ZW = distance YX, then △WXZ ≅ △XWY (SSS Property)
5	m∠ZWX = m∠YXW	if △WXZ ≅ △XWY, then m∠ZWX = m∠YXW (Congruent Triangles Property 5)
6	m∠ZWX = m∠WXY	if m∠ZWX = m∠YXW, then m∠ZWX = m∠WXY (Angle Symmetry Example)
7	WZ || XY	if WXYZ is a parallelogram, then WZ || XY (Parallelogram Property 3)
8	ZW || YX	if WZ || XY, then ZW || YX (Parallel Lines Property 2)
9	∠ZWX and ∠WXY are supplementary	if ZW || YX, then ∠ZWX and ∠WXY are supplementary (Interior Angles of Parallel Lines)
10	(m∠ZWX) + (m∠WXY) = 180	if ∠ZWX and ∠WXY are supplementary, then (m∠ZWX) + (m∠WXY) = 180 (Supplementary Angles Property)
11	(m∠WXY) + (m∠WXY) = 180	if (m∠ZWX) + (m∠WXY) = 180 and m∠ZWX = m∠WXY, then (m∠WXY) + (m∠WXY) = 180 (Substitution 8)
12	m∠WXY = 90	if (m∠WXY) + (m∠WXY) = 180, then m∠WXY = 90 (One Eighty 4)
13	∠WXY is a right angle	if m∠WXY = 90, then ∠WXY is a right angle (Right Angle Property (Converse))
14	WXYZ is a rectangle	if WXYZ is a parallelogram and ∠WXY is a right angle, then WXYZ is a rectangle (Parallelogram Property)

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