Step-by-step explanation:
to repeat : all 4 sides are equally long, and all angles between 2 sides are 90°.
a diagonal connects 2 opposing vertexes of the square.
that leaves 2 vertexes that then become the top vertexes of the triangles.
the 2 vertexes connected by the diagonal and one of these top vertexes create one triangle, and with the other top vertex a second triangle.
both triangles are isoceles triangles (both legs have the same length) with the length of their legs being the side length of the square.
the baseline of both triangles is the diagonal they both share.
so, all 3 sides are congruent between the 2 triangles.
that alone is already proof (SSS).
in addition we know that the angles at the top vertexes are 90°, because they are also the angles of the square.
and because they are isoceles triangles, the 2 angles at the baseline must be equal in both triangles. and due to the fact that the sum of all angles in a triangle must always be 180°, and one of these angles is 90° in both cases, these angles must be identical in both triangles.
so, they are congruent for every bit of triangle attribute.
