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Proof of Equilateral Triangle

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∆ABC is Equilateral
α∆ABC = x²√3/4
Step 1
Drop an altitude
Step 2
ISOBAM makes altitude an angle bisector
Step 3
Angle bisector makes the 60° angle into two 30° angles
Step 4
By definition, we now have a 30-60-90 triangle
Step 5
Because it is a 30-60-90, the height must be x√3/2 and the base must be ½x
Step 6
½b×h = x²√3/8
Step 7
Because there are two 30-60-90 triangles, we multiply by 2 to get the prove statement