Math Question

[shams]

Entroper said:

shams said:

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.

 

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.

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...