Is there something hidden?

[the arrow of egypt]

In the name of the Merciful Allah,
Hello there, please read the following phrases:
1-" An approach to psychology based on ......"
2-"Sigmund freud (1856-1939), shown here in the picture...."
3-"When presented with questions written on large cards, Hans would spell out answers by tapping......."
My questions are about : "based" in (1), "shown"in (2),"presented" and
"written" in (3). First,are they all the same in terms of their analysis?. Is there
something hidden before any one of them (like, that)?.
In fact, such way of writting has confused me alot. So ,please help me guys.

[Harry Smith]

In the name of the Merciful Allah,
Hello there, please read the following phrases:
1-" An approach to psychology based on ......"
2-"Sigmund freud (1856-1939), shown here in the picture...."
3-"When presented with questions written on large cards, Hans would spell out answers by tapping......."
My questions are about : "based" in (1), "shown"in (2),"presented" and
"written" in (3). First,are they all the same in terms of their analysis?. Is there
something hidden before any one of them (like, that)?.
In fact, such way of writting has confused me alot. So ,please help me guys.

1. psychology which is based on....
2. Sigmund Freud who is shown here in the picture...
3. When they are presented with guestions that are written on large cards,
Hans would spell out.....

[Anglika]

The last one should be "When he was shown the questions written onto large cards, Hans (the clever horse) ...."

[the arrow of egypt]

In the name of the Merciful Allah,
Many thanks to Harry and Anglika , I understand now that words " based",
"shown"and " written" are adjectives . Evidently, hiding both of pronoun (who or which)and verb (be) is possible in English. Could you please show me the underlying rule?.
About the word "presented ", I'm still confused . what's realy behind it ?.
To be more aware of its context , you can read this:"Nor were his presumed talents limited to math : When presented with questions written on large cards, Hans would spell out answers by tapping the groung to indicate letters on an alphabet board.

[the arrow of egypt]

Hello, let me rephrase my questions again. Are "based","shown","presented'
and"written" all past participal according to their context?. what is the underlying rule that allow us hiding words in English?

[Casiopea]

All the words in pink are past participles, and the "hidden" words are in bold:

1. An approach to psychology that is based on...
2. Sigmund Freud (1856-1939), who is shown here in the picture...
3. When Hans was presented with questions that were written on large cards, Hans would spell out answers by tapping...

Here's what's happening. In 1. and 2. the omitted words that is and who is are part of a relative clause.

that (subject) is (verb) based (past participle)
who (subject) is (verb) shown (past participle)

Each relative clause modifies a noun. The relative pronoun that stands for An approach and the relative pronoun who stands for Sigmund Freud.

An approach that is based on
Sigmund Freud, who is shown here

There's a redundancy there. Both the relative clause and the past participle housed inside it function as adjectives. The relative clause is reduced. The relative pronoun is omitted and, along with it, its verb is omitted too, which is why we end up with the past participle.

An approach based on
Sigmund Freud, shown here

All the best.

[Casiopea]

3. When Hans was presented with questions that were written on large cards, Hans would spell out answers by tapping...

In 3. the subjects are the same (Hans), which is why the first Hans and its verb (was) are omitted. Again, redundancy is the reason.

All the best.

[the arrow of egypt]

Wow,I'm really impressed by your replies. But don't you think that
redundancy is not the reason for omitting the verbs"is" and"were"?.
By the way, let me refresh your memory about asking me a day to summarize something for me in 27 of March?,check your posts.
Any way, thanks alot.