Proof: Equilateral Triangle 60

Let's prove the following theorem:

if △XYZ is an equilateral triangle, then m∠XYZ = 60

Proof:

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Given

1	△XYZ is an equilateral triangle

Proof Table

#	Claim	Reason
1	m∠XYZ = m∠YZX	if △XYZ is an equilateral triangle, then m∠XYZ = m∠YZX (Angles of an Equilateral Triangle 4)
2	m∠YZX = m∠ZXY	if △XYZ is an equilateral triangle, then m∠YZX = m∠ZXY (Angles of an Equilateral Triangle 3)
3	m∠XYZ = m∠ZXY	if m∠XYZ = m∠YZX and m∠YZX = m∠ZXY, then m∠XYZ = m∠ZXY (Transitive Property of Equality)
4	((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180	((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 (triangles_sum_to_180)
5	((m∠XYZ) + (m∠YZX)) + (m∠XYZ) = 180	if ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 and m∠XYZ = m∠ZXY, then ((m∠XYZ) + (m∠YZX)) + (m∠XYZ) = 180 (Substitute 2)
6	(m∠XYZ) + (m∠YZX) = (m∠XYZ) + (m∠XYZ)	if m∠XYZ = m∠YZX, then (m∠XYZ) + (m∠YZX) = (m∠XYZ) + (m∠XYZ) (Add Term to Both Sides 2)
7	((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = 180	if ((m∠XYZ) + (m∠YZX)) + (m∠XYZ) = 180 and (m∠XYZ) + (m∠YZX) = (m∠XYZ) + (m∠XYZ), then ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = 180 (Substitution 8)
8	((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = (m∠XYZ) ⋅ 3	((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = (m∠XYZ) ⋅ 3 (add_three)
9	(m∠XYZ) ⋅ 3 = 180	if ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = (m∠XYZ) ⋅ 3 and ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = 180, then (m∠XYZ) ⋅ 3 = 180 (Transitive Property of Equality Variation 2)
10	m∠XYZ = 180 / 3	if (m∠XYZ) ⋅ 3 = 180, then m∠XYZ = 180 / 3 (Divide Each Side)
11	180 / 3 = 60	180 / 3 = 60 (Fixed Value Statement)
12	m∠XYZ = 60	if m∠XYZ = 180 / 3 and 180 / 3 = 60, then m∠XYZ = 60 (Transitive Property of Equality)

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