# Euclid I-9. (pg 8)

- Author:
- Emily Crum

Explanation:
Let angle BAC be the rectilinear angle.
Create point D on BC. Then make pt. E on CA such that AD = AE.
Join pts. D and E together with a line segment.
Next create an equilateral triangle with DE. (This was done previously and does not need to be proven)
This equilateral triangle is triangle FDE
Connect F and A.
Triangles FDA and FEA are congruent because of SSS
AD = AE as per the earlier directions
AF = AF (AF is in common between the two)
and DF = EF because Triangle FDE is equilateral.
Because these two triangles are congruent, this means that all of their angles are congruent too
Thus, angle BAF = angle CAF.
Since the two angles equal each other, then Angle BAC has been bisected.