Pythagoras Triangles

Normal Sudoku rules apply. Numbers in cages sum to the number in the toip left corner of the cage. Numbers with a white dot between them are consecutive. Not all possible dots are shown. Numbers on triangles represent a unique right triangle for each color. The size of the triangle is found by ADDING the two numbers on each side to get a 3-4-5 triangle, a 6-8-10 triangle and a 9-12-15 triangle. The largest number added will always be the diagonal of the triangle. ONE OF THE COLORS IS A LIAR. The numbers on this color do not follow any of the above rules. ALL FOUR COLORS each have the same three numbers on them. All possible triangles are shown. Note for colorblind people: There are 8 Red, 5 Purple, 5 Blue, and 4 Yellow triangles shown.