How can a vegitarian who does not consume milk eggs or meat have complete proteins in there diet?

Vegetarians can have a well balanced, wholesome diet, given that they eat consciously healthy foods.

There is a myth that vegetarians and vegans lack "complete proteins" because they do not consume meat. So how did this myth come about?

In 1914, Thomas B. Osborne and Lafayette B. Mendel conducted studies on rats, which suggested that they grew best when fed a combination of plant foods whose amino acid patterns resembled that of animal protein. That makes sense, as all baby mammals, rats and humans included, grow best when fed the perfect food for baby mammals: their mother's milk. The term "complete protein" was coined to describe a protein in which all eight or nine essential amino acids are present in the same proportion that they occur in animals. "Incomplete protein" described the varying amino acid patterns in plants. It's a misleading term, because it suggest that humans (and other animals, one would assume) can't get enough essential amino acids to make protein from plants.

Fortunately, the theory that plant proteins are somehow "incomplete" and therefore inadequate has been disproven. All unrefined foods have varying amounts of protein with varying amino acid profiles, including leafy green vegetables, tubers, grains, legumes, and nuts. All the essential and nonessential amino acids are present in any single one of these foods in amounts that meet or exceed your needs, even if you are an endurance athlete or body builder.