Chapter F.1, Problem 56AYU

Geometry Verify that the points $\left(\frac{a}{2},\frac{\sqrt{3}a}{2}\right)$ 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 (refer to problem 54).