Edit: Hid the answer 
They aren't triangles, but rather very cleverly constructed quadrilaterals. For the whole shape to be a triangle, the two inner triangles must have the same angled hypotenuse, yet a simple ratio calculation shows this is impossible:
Smaller triangle: 5 units width : 2 units height.
Larger triangle: 8 units width : 3 units height.
5:2 is not the same ratio as 8:3, so the angle of the hypotenuse is different. The equation for finding the angle is:
tan(θ) = opposite / adjacent
so in the smaller triangle, this would be: tan(θ) = 2 / 5
in the larger, this would be tan(θ) = 3 / 8
As 5:2 and 8:3 are not equivalent ratios, their inverse cannot be either, so the tan(θ) will be different each time.
In the first triangle, the hypotenuses bend in towards the rest of the shape. In the second, they bend outwards, creating the extra square.
They aren't triangles, but rather very cleverly constructed quadrilaterals. For the whole shape to be a triangle, the two inner triangles must have the same angled hypotenuse, yet a simple ratio calculation shows this is impossible:
Smaller triangle: 5 units width : 2 units height.
Larger triangle: 8 units width : 3 units height.
5:2 is not the same ratio as 8:3, so the angle of the hypotenuse is different. The equation for finding the angle is:
tan(θ) = opposite / adjacent
so in the smaller triangle, this would be: tan(θ) = 2 / 5
in the larger, this would be tan(θ) = 3 / 8
As 5:2 and 8:3 are not equivalent ratios, their inverse cannot be either, so the tan(θ) will be different each time.
In the first triangle, the hypotenuses bend in towards the rest of the shape. In the second, they bend outwards, creating the extra square.
