Chapter 1.1, Problem 72AYU

Challenge Problem Geometry Verify that the points $\left(0,0\right)$, $\left(a,0\right)$, and $\left(\frac{a}{2},\frac{\sqrt{3}a}{2}\right)$ are the vertices of an equilateral triangle. Then show that the midpoints of the three sides are the vertices of a second equilateral triangle.