Question 1023683
<pre>{{{drawing(400,400,-1.1,1.1,-1.1,1.1,
locate(-.4,.5,A),locate(0,.5,B),locate(.4,.5,C),
locate(-.4,.1,D),locate(0,.1,E),locate(.4,.1,F),
locate(-.6,-.3,G),locate(-.2,-.3,H),locate(.3,-.3,I),locate(.6,-.3,J),
locate(0,-.6,K),

line(0,1,-0.95105652,0.30901699),
line(-0.95105652,0.30901699,-0.58778525,-0.80901699),
line(-0.58778525,-0.80901699,0.58778525,-0.80901699),
line(0.58778525,-0.80901699,0.95105652,0.30901699),
line(0.95105652,0.30901699,0,1),

line(0,1,-0.95105652,0.30901699),line(0,1,-0.58778525,-0.80901699),line(0,1,0.58778525,-0.80901699),line(0,1,0.95105652,0.30901699),line(-0.95105652,0.30901699,0,1),line(-0.95105652,0.30901699,-0.58778525,-0.80901699),line(-0.95105652,0.30901699,0.58778525,-0.80901699),line(-0.95105652,0.30901699,0.95105652,0.30901699),line(-0.58778525,-0.80901699,0,1),line(-0.58778525,-0.80901699,-0.95105652,0.30901699),line(-0.58778525,-0.80901699,0.58778525,-0.80901699),line(-0.58778525,-0.80901699,0.95105652,0.30901699),line(0.58778525,-0.80901699,0,1),line(0.58778525,-0.80901699,-0.95105652,0.30901699),line(0.58778525,-0.80901699,-0.58778525,-0.80901699),line(0.58778525,-0.80901699,0.95105652,0.30901699),line(0.95105652,0.30901699,0,1),line(0.95105652,0.30901699,-0.95105652,0.30901699),line(0.95105652,0.30901699,-0.58778525,-0.80901699),line(0.95105652,0.30901699,0.58778525,-0.80901699)  )}}}

There are 5 sets of congruent triangles.

I have lettered all 11 regions A through K.
I will indicate triangles by writing the regions
which they contain, such as A represents triangle
whis is just region A.  AB will represent the
triangle composed of regions A and B.  ABC will
represent the triangle composed of regions A,B,
and C.  ABDEI is the triangle composed of regions
A,B,C,D,E, and I.

1. These 5 triangles are congruent: A&#8773;C&#8773;G&#8773;J&#8773;K
2. These 5 triangles are congruent: B&#8773;D&#8773;F&#8773;H&#8773;I
3. These 10 triangles are congruent: 

AB&#8773;BC&#8773;CF&#8773;FJ&#8773;IJ&#8773;IK&#8773;HK&#8773;GH&#8773;GD&#8773;AD
 
4. These 10 triangles are congruent: 

ABC&#8773;ADG&#8773;GHK&#8773;KIJ&#8773;CFJ&#8773;DEF&#8773;BEH&#8773;DEI&#8773;EFH&#8773;BEI

5. These 5 triangles are congruent: ABDEI&#8773;BCEFH&#8773;DEFIJ&#8773;BEHIK&#8773;DEFGH

That makes 35 triangles.

They are congruent by the law of common sense of symmetrical
things. [Yes I know that's not a proof! :)  ]

It wouldn't be hard to prove any two of those congruent, but
all 35?  Forget it!  If you pick two that you want me to
prove congruent, I can help you do that, but proving that 
all pairs of congruent triangles above are really congruent 
is an unreasonable task that would take many hours.

Edwin</pre>