As shown in the figure, rotate the right triangle abd 90 counterclockwise around the right vertex a to the position of the triangle ACF. The triangle abd is equal to the triangle ACF. The extension of BD intersects CF with point E and connects BC. If the angle FBE = angle CBE, try to determine the relationship between CE and BD (including the position relationship and quantity relationship),

As shown in the figure, rotate the right triangle abd 90 counterclockwise around the right vertex a to the position of the triangle ACF. The triangle abd is equal to the triangle ACF. The extension of BD intersects CF with point E and connects BC. If the angle FBE = angle CBE, try to determine the relationship between CE and BD (including the position relationship and quantity relationship),

The positional relationship between CE and BD is vertical, and the quantitative relationship is BD = 2ce. The proof is as follows: because △ abd ≌ △ ACF, so ∠ Abe = ∠ ACF, BD = CF because ∠ BAC is right angle, so ∠ caf ＋ f = 90, so ∠ Abe ＋ f = 90, so ∠ bef = 90, so be ⊥ CF, that is, CE ⊥ BD, so ∠ BEC = ∠ bef =