It is known that in square ABCD, ∠ man = 45 ° and ∠ man rotates clockwise around point a, and its two sides intersect CB and DC (or their extension lines) at points m and N respectively. When ∠ man rotates around point a to BM = DN (as shown in Figure 1), it is easy to prove that BM + DN = Mn (1) When ∠ man rotates around point a to BM ≠ DN (as shown in Figure 2), what is the quantitative relationship among BM, DN and Mn? Write out the conjecture and prove it; (2) when ∠ man rotates around point a to the position as shown in Fig. 3, what is the quantitative relationship among line segments BM, DN and Mn? Please write your guess directly
(1) BM + DN = Mn is true. It is proved that: as shown in the figure, △ adn is rotated 90 ° clockwise around point a to get △ Abe, then E, B and m are collinear (the drawing is correct). In △ AEM and △ anm, AE = an ∠ EAM = namam