# Euclid I-31. (pg 24)

- Author:
- Emily Crum

Explanation:
Construct line BC and pt A. Pick pt D on BC and connect AD.
Create angle DAD' such that it is equal to angle ADC.
Connect D' to F forming line D'F.
D'F is parallel to BC because angle DAD' = angle ADC and AD acts as a transversal, thus they are equal by alternate interior angles. Thus BC is parallel to D'F.