First, you should ask questions properly. Beginning with "write a program that prints the following patterns" sounds like you're issuing orders, not asking for help.
Second, to do that, you need two for loops, as your title points out. The outer one should determine how far the inner one will go:
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int i, j;
for(i = 0; i < SIZE; ++i) {
for(j = 0; j <= i; ++j) {
printf("*");
}
printf("\n");
}