Composite Shapes (1)
There are only two kinds of three-tile composite shapes: the pair + taatsu composite, and the ryan-kan composite.
Pair-and-Taatsu Composite Shapes
This was mentioned briefly in the section on pairs. It is a shape where one tile of a taatsu is duplicated into a pair. Compared with an ordinary taatsu, it gains two extra tiles of acceptance that complete a triplet.
| Type of composite | Example | Tiles that complete a set | Count |
| Penchan + pair |   |
 |
6 |
| Kanchan + pair |   |
 |
6 |
| Ryanmen + pair |   |
  |
10 |
With shapes like these, many players fix them too early as either a pair or a taatsu. If you fix them as a pair, you lose 4 tiles of acceptance, or 8 in the ryanmen case. If you fix them as a taatsu, you lose 2 to 4 tiles.
Example 1 
Tsumo
Beginners often seem to prefer pairs for some reason.
From a shape like this, you sometimes see people cut ,
but that throws away the 4-tile acceptance of 
and also kills the chance for the pinzu shape to improve.
It is not good play.
It may feel like losing 2 or 4 tiles is not a big deal. But mahjong is heavily a race in tenpai speed, so if all you are doing is narrowing your acceptance, it is clearly a loss.
The standard play is to discard .
Example 2 
Tsumo
In a shape like Example 2, leading with is also a mistake in most cases.
The hand currently has only 16 tiles of acceptance,
so reducing that to 12 is a very large loss.
On top of that, this hand can become Tanyao and still has pon-ten potential,
so unless is especially awkward to deal with in the current situation,
you should simply discard .
Theory and Summary
Ryan-Kan
A shape formed by two connected kanchan shapes is called ryan-kan.
There are five such ryan-kan shapes, and all of them have 8 tiles of acceptance, exactly twice that of an ordinary kanchan.
If you look only at the number of accepting tiles, ryan-kan has the same 8 tiles as ryanmen, so it counts as a good shape. However, depending on how it interacts with the rest of the hand, ryan-kan can become awkward.
Example 3 
Tsumo
In Example 3, if you care only about the fastest route to tenpai, then keeping the ryan-kan and cutting is the closest line.
But that throws away the yaku Ittsuu.
And if the souzu ryanmen fills in first, the final wait is only an ordinary kanchan anyway.
Example 4 
Tsumo
Example 4 is one of those difficult cases where every discard loses something.
Both of these shapes look like they can make you hesitate. Because ryan-kan uses three tiles, it tends to make the hand feel tighter and tighter as you approach tenpai. Of course, some of that cannot be avoided.
Theory and Summary
Original Japanese page: http://beginners.biz/kihon/kihon09.html