Take 0.1717...to be x multiply by 100 on both sides thus we have, 100x = 17.1717... But we know that 0.1717 = x (Look at the 1st line) Thus we have, 100x = 17 + x 100x - x = 17 99x = 17 x = 17/99' It cannot be 77/99.  

Take 2 II gm's abcd,abef on the same base and between the same parallels. Cut triangle BEC and paste it on triangle AFD. Thus it gets proved