Question

what shows homologous chromosomes

Answer 1

Karyotypes show them.

HOMOLOGOUS chromosomes are like...chromosome partners.

If two chromosomes are HOMOLOGOUS,
it means that they are the same length,
and their centromeres are in the same places, as one another's centromeres.

A KARYOTYPE is a chart, that shows all of an organism's chromosomes.
Like this chart:
http://4.bp.blogspot.com/_uMaVYaKgEKc/TJoqqhZ1VRI/AAAAAAAAAE0/yaKMUCAobA0/s1600/Human+karyotype.jpg

The chromosomes are all listed in homologous pairs.

Like take a look at Group #1.
There are two chromosomes, in Group #1.
And they're both HOMOLOGOUS,
because they're about the same size.

You see?