Question

what is meant by analogous organs ? take a suitable example , explain how they support theory of organic evolution

Answer 1

                                    Analogous organs :
JUST DON'T PANIC BY SEEING THIS .CALM DOWN AND READ ON FOR EXPERTISING IN THIS TOPIC

(i am giving my answer with reference to the biology student of high school standard who has read evolution even once
in case of any doubts you can ask me........dont worry i am using very simple terms and making it so easy to understand calm down and read if in case of difficulty contact me)

Analogous organs:    
They SIMILAR FUNCTIONS ,BUT DIFFERENT STRUCTURES

example:   the pretty  and thin wings of a butterfly with vivid difference of a bird's wing they are completely different from one and another but their function flying is still the same , a bird can fly as well as a butter fly can


to be more convincing this is just like the food we order in  hotel we eat different things  with different structure but no mater what they are they serve a similar function filling our tummies lol
(just for understanding purpose)

The butterfly and bird wing example i said above is a perfect example for anologous organs and convergent evolution------infact they are a result of convergent evolution
let me explain you about convergent evolution along with the relation of the organic theory:

when any organism is subjected to an environment it tries to make it self suitable to the environment to survive .It evolves itself making it sustainable just  making the two different organisms  come closer in the relations by the structures they evolve it even makes the difference between the same organisms too
just like the finches in the Galapagos island and the Australian marsupials
they all are analogous and they are all doing convergent evolution.

STILL DIDNT GET IT HERE'S YOUR ANSWER:
ORGANIC EVOLUTION THEORY:
This theory states the scenario where an organism develops according to the environment for its survival purposes . It evolves its features and structure to the changes in the environment

there are several examples for these:    ( but let me explain these examples with reference to analogous organs with regard to your concern)

1.)the finches in the galapagos island is one of the best example for analogous organs and convergent evolution they all are making thier self suitable tot he environment and they all serve a similar function of feeding

2.) the wings of the butterfly and the bird is of same case

for further queries comment below:
courtesy:fire furry:)

Answer 2

Analogous organs are defined as the structures that differ in their basic structures or developmental origin but appear similar or perform similar functions. The most common example is the wings of bat and wings of bird. They perform similar functions i.e. help the organism to fly, but there structure is different. Bat wings are made up of flaps of skin which is stretched between the bones of the fingers and the arm while the wings of bird are made up of feathers extending all along the arm. 

Presence of analogous structures supports the process of convergent evolution, where unrelated organisms develop similar characteristics to adapt to similar environments. 

hope it may help you