What do the following words have in common?

AGE
GRACE
SEDENTARY

HINTS:
#1: The answer will make the first two words almost rhyme.
#2: The same two letters will change each word into a new one.

Answer:

The letters IM can precede or be inserted into each word to make a new one:

IMAGE
GRIMACE
SEDIMENTARY 

Credit: NY Times Crossword
March 6, 2008 
Pamela Amick Klawitter