Question

In triangle ABC, let D be on AB and E be on AC such that DE is parallel to BC. Let DC and BE intersect at H and AH extended intersects BC at F. Prove F is the midpoint of BC.

Answer 1

do you have a drawing?

Answer 2

no

Answer 3

ok got a drawing

Answer 4

and DE is parallel to BC

Answer 5

ok let me think

Answer 6

may i add that bcde is a trapezoid, with dc and be as diagonals

Answer 7

that is true

Answer 8

maybe i could prove af is a median?

Answer 9

yeah that's essentially what they want, but I'm trying to remember how to do it. hmm

I remember seeing a proof for it

Answer 10

all i know right know is that triangles dhe and chb

Answer 11

are similar

Answer 12

that is correct

Answer 13

since these pairs of angles are congruent