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

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