It is known that the vertex a of RT △ ABC is the intersection point of the first quadrant of the image of the linear function y = x + m and the inverse scale function y = m / x, and s △ AOB = 3. If the extension of the line AC intersects another branch of the image of the inverse scale function at point D and makes the de ⊥ X axis at e through D, please judge which special triangle △ AOD is and prove it

It is known that the vertex a of RT △ ABC is the intersection point of the first quadrant of the image of the linear function y = x + m and the inverse scale function y = m / x, and s △ AOB = 3. If the extension of the line AC intersects another branch of the image of the inverse scale function at point D and makes the de ⊥ X axis at e through D, please judge which special triangle △ AOD is and prove it

an isosceles triangle
prove:
On the symmetry of inverse proportion function in y = - x
And y = x + m is perpendicular to y = - X
That is y = - x vertical bisector ad
So Ao = OD