I am currently reading about the ratios of the sides of triangles.
By basic proportionality theorem, I was able to prove that if DE || BC in a given triangle ABC, then: AD/DB = AE/EC
And by triangles similarity, I was able to prove that if DE || BC in a given triangle ABC, then: AD/AB = AE/AC
But I am still confused. I was told by someone(I don't remember who told me) that if DE || BC in a given triangle ABC, then: AD/DB=DE/BC.
But there is really no way, I can think that this is true. I tried very hard to prove this but I failed. As a last try, I want to know is this really true or am I just wasting time proving this.