Proof: If Isosceles Trapezoid Then Diagonals Congruent

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	m∠ZWX = m∠YXW	if quadrilateral WXYZ is an isosceles trapezoid, then m∠ZWX = m∠YXW (If Isosceles Trapezoid Angles Congruent 2)
2	distance WZ = distance XY	if quadrilateral WXYZ is an isosceles trapezoid, then distance WZ = distance XY (Isosceles Trapezoid Property)
3	distance ZW = distance YX	if distance WZ = distance XY, then distance ZW = distance YX (Distance Property 3)
4	distance WX = distance XW	distance WX = distance XW (Distance Equality Property)
5	△ZWX ≅ △YXW	if distance ZW = distance YX and m∠ZWX = m∠YXW and distance WX = distance XW, then △ZWX ≅ △YXW (SAS Property)
6	distance XZ = distance WY	if △ZWX ≅ △YXW, then distance XZ = distance WY (Congruent Triangles Property 9)
7	distance WY = distance XZ	if distance XZ = distance WY, then distance WY = distance XZ (Symmetric Property of Equality)

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