Question about Similar shapes. Help pls!!

Question

I have a diagram, it has a straight line parallel to the base BC of the triangle ABC meets AB and K and AC at L.

i) I need to prove that triangles AKL and ABC are similar

ii) If KL:BC = 3:4 i need to find the ratio AK:KB

Answer 1

Use AAA to prove similarity (parallel lines cut by a traversal have equal corresponding angles.

AK:KB = 3:4.Corresponding parts of similar polygon are in proportion