## Posts Tagged ‘**construction**’

## Round 4: Problem 2 Solution

Here’s a geometric construction proof:

- Extend and so that they intersect at an exterior point .
- Extend and in a similar fashion so they intersect at another exterior point, , forming quadrilateral .
- since each external angle is supplementary with the 60 degree internal angle.
- , so are equilateral triangles.
- in equilateral triangles.
- is a parallelogram (both pairs of opposite angles are congruent), so .
- , so by equilateral triangles as shown above.

Advertisements