# Answer to the first challenge by Anthony OR - GGG 2015

- Author:
- Irina Boyadzhiev

Problem:
Given are three parallel lines and . Construct an equilateral triangle such that each of its vertices is on one of the lines.
Solution:
For any equilateral triangle a rotation with center one of the vertices and angle will map one of the remaining vertices onto the third vertex.
Let be an arbitrary point on line .
is on line , then the third vertex of the triangle should be on the image of line , but it also has to be on the third line . Therefore, vertex is the intersection point of the lines and . This way we find two vertices and determine the side of the equilateral triangle.
and degrees.

- Drag the slider to the end to rotate line
on angle around point .

- Click on the Construction button to finish the construction.

- Drag the gray points to change the positions of the lines.
- What do you notice when line
is above line or below line ?

*Geometric Transformations*I, MAA, 1962, Chapter 2, Problem 18