You want one convincing proof? Consider this:
I'm sure you've heard that humans and chimpanzees have the vast majority of our DNA in common. You're also probably not convinced by this argument ("I don't understand...so what if two organisms share the same genes? How does this prove that they came from the same lineage?"). But for now, forget about how very similar we are in our genetic sequence and let's focus on our chromosomes.
If you need a refresher, remember that the number of chromosomes a species has tends to stay the same from generation to generation. A fruit fly has four autosomal chromosomes and one pair of sex chromosomes; it's offspring will all have the same number. What about us humans? We have 23 pairs of chromosomes; 46 chromosomes in total. If you took a karyotype - that's a display of all the chromosomes in a cell - of an ape (I know you're skeptical of humans being primates, but lets call 'em primates for now) you'll notice something different from human chromosomes: there's two extra! Apes have 48 chromosomes.
You might wonder how this proves we evolved from an ancestral primate. You might even suspect that it is evidence against such a claim, since an ancestral primate would have had 48 chromosomes, and that number would have likely stayed constant down the generations, while in us, it's different. Well, this information alone does not prove much. But let's take a look at what the genome sequence shows us.
The sequence of the human genome showed an interesting fact about our Chromosome 2. The area around the very centre of chromosome 2 (known as a centromere) looked an awful lot like telomeric DNA. Telomeres are the regions at the very ends of chromosomes; what were they doing in the centre of chromosome 2? Furthermore, each arm of Chromosome 2 had what appeared to be their own centromeres. Chromosome 2 was looking to be quite an oddity. No other human chromosome displayed these characteristics.
Once the chimpanzee genome was sequenced, things got even more interesting. One of the chimpanzee's chromosomes was pretty much identical to the top half of the human Chromosome 2. Another chimpanzee chromosome was nearly identical to the bottom half of Chromosome 2. On top of this, the banding pattern of these two chromosomes (as well as the same chromosomes in many other species of primates) was a complete match to the banding pattern of Chromosome 2.
Coincidence? Not likely. What this is, is evidence of a chromosomal fusion. An ancestral primate, ancestor to humans, chimpanzees and apes, had 24 pairs of chromosomes. Eventually, this lineage diverged: apes and chimps went one way and we humans evolved along a separate path. But something interesting happened in the lineage that was to become humans: the two extra chromosomes from that ancestor fused together end to end to become human Chromosome 2. This is why our Chromosome 2 has what appears to be telomeres in its centre, and what appears to be two extra centromeres, one on each arm.
The only way to explain Chromosome 2's odd characteristics and similarity to other primates is with a chromosomal fusion. And the only way this could be possible is if we were descended from a common primate ancestor.
So, I put the question to you: if you could give only one single line of evidence for man's primate ancestry to change a creationist's mind, what would it be?