basic proportionality theorem
We can see a triangle ABC. m and m_1 are the slopes of the line segments BC and DE respectively. Observe how the shape of the triangle gets changed when we move the points A, B, C. When points D and E are moved, then m_1 will change.
Questions to think about Move the points B, C, D and E such that m=m_1 (parallel). What do we observe? For hint calculate DA/BD=EA/CE.