Evolution

During his voyage Darwin observed small black birds on the Galapagos Islands, later called Darwin's finches.
He found many varieties of finches on the same group of islands, and concluded that all of them had evolved on the islands themselves from one original seed-eating stock.
From the seed-eating features, many other forms with altered beaks arose, enabling them to become insectivorous and vegetarian finches.
This process of evolution of different species in a given geographical area, starting from a point and literally radiating to other areas of geography (habitats), is called adaptive radiation.
Another example is the Australian marsupials.
So Darwin's finches are an excellent example of adaptive radiation.

Homologous organs are organs that have the same basic structure and origin but perform different functions.
The thorn of Bougainvillea and the tendril of Cucurbita both arise in the axillary position and both are modifications of the stem (axillary bud).
The thorn is used for protection, while the tendril is used for climbing.
Since their origin is the same but their functions are different, they are homologous organs.
Homology indicates common ancestry and is the result of divergent evolution.
Analogous organs, in contrast, have different origins but perform similar functions, for example the wings of a butterfly and of a bird.

August Weismann proposed the theory of continuity of germplasm. According to it, the body has two kinds of protoplasm, the germplasm (in the germ cells) and the somatoplasm (in the body cells).
Only the changes in the germplasm are transmitted to the next generation, and the germplasm passes continuously from one generation to the next. This disproved the inheritance of acquired characters. So this pair is correctly matched.
Hugo de Vries proposed the mutation theory; the theory of natural selection was given by Charles Darwin.
The theory of pangenesis was given by Darwin; Mendel gave the laws of inheritance.
The inheritance of acquired characters was proposed by Lamarck; Louis Pasteur disproved spontaneous generation and gave the germ theory of disease.
So the correct match is Weismann - Theory of continuity of germplasm.