Ugb, we are on a sales analasis site, isn't there someone who can explain it better than me. The do share 1 angle. The angles in the middle are the same because the lines creating them both continue on from one triangle to the next. In math that is enough so that we can declare them the same.

Kruze S is right. Assuming they both share the same angles, they would be congruent. However, since the diagram doesn't display angles, you'd have to make a best guess that they both have a right angle, and therefore they are indeed congruent. If you really want to know, print out the page and cut out the triangles and lay them over top =)

There are a few incorrect statements here.

Kruze S is correct that they have to share two sides and an angle, but the tricky part is that the angle must be the one between the two sides.  In this case, the angle between the two sides is not marked.  If we could assume that it is a right angle, we could say the triangles are congruent.

We do know that the triangles have an equal angle where they touch, thanks to the concept of opposite angles, but this is not sufficient to prove the triangles are congruent. 

Assuming they are right-angled triangles, they are definitely congruent ;)

When 2 sides of a triangle, and the angle between them are equal (across 2 or more tris) - the triangles are identical.

Its quite common to leave the "right-angle" visual indicator out - but it should be included for completeness.

EDIT - actually, slightly incorrect. The 3rd side (the unmarked one) of the triangle HAS to be the same length in both tris - because they intersect halfway exactly. So you don't even need to have the right-angle indicator - its implicit.

You don't even need to go that far, assuming the straight vertical lines are the same line and the diagonal lines are the same line then the || and the | are enough to say that the triangles are congruent.

BTW, 3rd side is also identical on both tri's thanks to Pythagoras: a^2 = b^2 + c^2 (b & c are same length for both tris, hence a is well)

How do you know that they intersect halfway?  You know that the horizontal line is cut halfway, but that doesn't tell you much about the diagonal line.

Pythagoras only works for right triangles, so again, that only works if you assume that these are right triangles.

Wow, a lot of you still know your Math. Impressive.

Good point about pythagoras - been too long, and always assume I'm working with 90deg tri's ;)

Halfway? This is why...

The intersecting lines are both straight lines (assume so - at least from the picture, if not then...).

The smallest angle in both triangles is equal (basic geometry - can't remember the name of the rule...).

...

Now from here, I can't remember the exact rule - but if 2 sides & 1 angle in both triangles are equal - the triangles are equal/congruent. If you look at it on paper, its obvious - with 2 sides alone that are equal, there are an infinite number of solutions - but only 1 solution where one of the angles is equal.

So all 3 sides are equal, and the longest side must be split halfway by the intersection point. 

(I always enjoyed maths, but geometry was my weakest topic.. :<)

Anyway...

The problem is that we can't assume things from eyeballing them. Let's say the "right" angle in the left triangle is really 92 degrees, and the "right" angle in the right triangle is 88. You'd end up with the same line, shifted up and left, still bisecting the horizontal line, but the diagonal would be longer on the left side than the right. It can't be proven or disproven without more info.