Proof: Right Angle in Equilateral

Let's prove the following theorem:

if △XYZ is an equilateral triangle and M is the midpoint of line XY, then ∠XMZ is a right angle

Z X M Y

Proof:

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Given
1 △XYZ is an equilateral triangle
2 M is the midpoint of line XY
Proof Table
# Claim Reason
1 distance XZ = distance YZ if △XYZ is an equilateral triangle, then distance XZ = distance YZ
2 m∠XMZ = 90 if distance XZ = distance YZ and M is the midpoint of line XY, then m∠XMZ = 90
3 ∠XMZ is a right angle if m∠XMZ = 90, then ∠XMZ is a right angle

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