The molecular evidence is far more sophisticated and compelling than mere similarity between genomes of related species.
Go here for evidence for how the human chromosome 2 is a fusion of two ancestral chromosomes, still separate in other great apes:
Chromosome fusion
Go here for a detailed explanation of how the comparisons between the mouse and the human genomes point inexorably to common descent:
Mouse genome home
For example: 'The rate of substitutions in ancestral repeat sequences in non-coding DNA is the same as the rate of substitution at four fold degenerate sites in functional regions - very strong evidence for mutation and selection over a long time.' There is much more evidence posted at the above URL and other pages at the same site that it links to.