1. What do the following words have in common?

LAPS
CORPS
FLU
PLUM
SUIT

2. What do the following words have in common?

ALLOW
EAVE
AUNT
EIGHT
EDGE

Answers:

1. The letter E can be added to the end of each word to form a new one:

LAPSE
CORPSE
FLUE
PLUME 
SUITE 

2. Each word can be preceded by H to make a new word:

HALLOW
HEAVE
HAUNT
HEIGHT
HEDGE