On a given finite straight line to construct an equilateral triangle.

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StepDescriptionJustification
1
Let $AB$ be the given straight line.
2
Draw $\odot BCD$ with center $A$ and radius $AB.$
P3
3
Draw $\odot ACE$ with center $B$ and radius $AB.$
P3
4
Draw $AC.$
P1
5
Draw $BC.$
P1
6
$AB = AC$ since both are radii of $\odot BCD.$
D15:2,4
7
$AB = BC$ since both are radii of $\odot ACE.$
D15:2,5
8
$AC = BC$
N1:6,7
9
$\triangle ABC$ is equilateral.
D20:6,7,8
QED