On the site of right triangle ABC, the angle bisector AE of ∠ B = 90 ° AB = AC intersects at point E Party A and Party B start from a at the same time and go along the AC and A-B-E lines at the same speed. Party A's destination is C and Party B's destination is e. please judge which of Party A and Party B arrive at their respective destinations first? And explain the reason

On the site of right triangle ABC, the angle bisector AE of ∠ B = 90 ° AB = AC intersects at point E Party A and Party B start from a at the same time and go along the AC and A-B-E lines at the same speed. Party A's destination is C and Party B's destination is e. please judge which of Party A and Party B arrive at their respective destinations first? And explain the reason

It is proved that: in F △ Abe and △ AFE, if we make ef ⊥ AC through e, we can make ∠ BAE = ∠ FAE (AE is the angular bisector of ∠ cab) ∠ B = ∠ AFE = 90 ° AE = AE, so △ Abe ≌ △ AFE, so AF = AB, EF = be ∠ C = 45 ∠ EFC = 90 ° cfcf = be