If P is any point on side AB of triangle ABC and F, K, E are the midpoints of AP, PB, and PC, prove that triangle FKE is similar to triangle ABC

Question

Please write a two-column proof. Also, there should ONLY be one given.

Answer 1

Draw and label a diagram.

FK = 0.5 AB Use the midpoints

FE = 0.5 AC FE || to AC at at midpoints

EK = 0.5 BC Same reason

FKG ≈ ABC

SSS

QED