Question: I discovered [here](http://smallpuzzlecollection.blogspot.ch/2016/04/of-symmetry-and-shapes.html) the Four Triangles Five Shapes puzzle (from Emrehan Halici).

[![ftfs](https://i.stack.imgur.com/087Ar.jpg)](https://i.stack.imgur.com/087Ar.jpg)

From the $4$ triangles, we can form:

— $3$ different parallelograms

— a square

— an isoceles triangle

The sizes and angles of the triangles are *approximatively*:
1) top left $a=7.5$cm, $b=7.8$cm, $c=3.2$cm ; $80°$ between $a,c$, $25°$ between $a,b$, $75°$ between $c,b$.

2) top right $a=4$cm, $b=5$cm, $c=3.7$cm ; $80°$ between $a,c$, $\sim 48°$ between $a,b$, $\sim 52°$ between $c,b$.

3) bottom left $a=10.5$cm, $b=8.3$cm, $c=4$cm ; $\sim 47°$ between $a,c$, $20°$ between $a,b$, $\sim 113°$ between $c,b$.

4) bottom right $a=7.5$cm, $b=7.5$cm, $c=2$cm ; $85°$ between $a,c$, $15°$ between $a,b$, $80°$ between $c,b$.

I could get none of them… So do you have a hint for some of them?

Thank you very much!

Answer: 
Based on the measurements in Jerry Loo's answer, I get the following lengths and angles for each of the original triangles:

```
Shape  -------Side (cm)--------    ------Angle (degrees)------
       a         b        c        A (^bc)   B (^ac)   C (^ab)
1      10.1      9.8      2.6      89.1      76.0      14.9
2      9.9       9.9      5.1      75.1      75.1      29.9
3      12.2      9.9      5.1      104.2     51.9      23.9
4      12.3      9.85     7.25     90.7      53.2      36.1

```

From which I can make the following shapes (in MS Paint, so proportions aren't entirely correct) -

Square:

[![Square](https://i.stack.imgur.com/NXv3q.png)](https://i.stack.imgur.com/NXv3q.png)

Parallelogram 1:

[![Parallelogram 1](https://i.stack.imgur.com/aIdZJ.png)](https://i.stack.imgur.com/aIdZJ.png)

Parallelogram 2:

[![Parallelogram 2](https://i.stack.imgur.com/rBZIh.png)](https://i.stack.imgur.com/rBZIh.png)

Parallelogram 3:

[![Parallelogram 3](https://i.stack.imgur.com/H53z7.png)](https://i.stack.imgur.com/H53z7.png)

Isosceles Triangle:

[![Isosceles Triangle](https://i.stack.imgur.com/1pG5W.png)](https://i.stack.imgur.com/1pG5W.png)
I reviewed Emrehan Halici's 4 piece triangle puzzle on my blog mentioned here. I am not good at such puzzles so it was rather difficult for me and even the one solution which I thought I got turned out to be wrong, when I asked Halici for and saw the solutions to the rest.

All the 4 solutions to the four problems do not contain holes in them, nor do they overlap..they are just placed side by side flat on a surface (no gaps) to form the 5 shapes required, all 2D, no 3D no tricks...seems easy when you look at the solutions with hindsight. 

If you want the dimensions and angles, its best you contact Halici directly. I have left a reply to the comment made by one of your members on my blog. Please PM me and I will ask if Halici is willing to allow a direct email to him for specs, info, etc...

At this year's IPP36 this past August in Japan, we exchanged puzzles and his puzzle is again one of these several-pieces-make-shapes type puzzle. I will post a write up on my blog in due course.

This is a very interesting forum/site relating to puzzles and I am learning a lot. Thanks

Jerry