The pyramid builders of ancient Egypt certainly knew about the 3-4-5, as they used a wooden version to measure right angles.
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Right angled triangles!
Right-Angle triangles
you can't, because the Pythagorean theorem is for right triangles and the triangles formed by the diagonal of a parallelogram are not right triangles.
Only right triangles.
The congruence theorems for right triangles are the Hypotenuse-Leg (HL) theorem and the Leg-Acute Angle (LA) theorem. The HL theorem states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. The LA theorem states that if one leg and one acute angle of one right triangle are congruent to one leg and one acute angle of another right triangle, then the triangles are congruent.