Question

Biped : quadruped :: ostrich :

Answer 1

Biped : quadruped :: Ostrich : Cheetah

Any animal from the cat family like the cheetah or the leopard can be considered as the answer.

A biped is an animal that uses two legs for walking and the quadrupeds are animals that use four legs for walking.

Ostriches and Cheetahs have long legs and similar ways of running fast and using their claws. Therefore, the cheetah can be considered as the best choice for the quadrupeds against ostrich as the biped.

Answer 2

Biped are the animals who have two feet in order to walk as well as run. 
While on the other hands quadruped word is used for the four legs animals .
As the ostrich is comes in category of two legs animals. Any four legs animal can be written next like
Biped: Quadruped ::Ostrich: Cat.
You can also write name of Dog, cow ,lions as well as tiger etc.
Interestingly, sometime the word quadruped is specifically  used for the horses.