(1) When the moving point p falls in the part of 1, it is proved that: angle APB= angle PAC+ angle PBD;;
(2) Whether the angle APB= angle PAC+ angle PBD holds when the moving point P is divided into two;
(3) When the moving point P is divided into three parts, fully explore the relationship between angle APB= angle PAC+ angle PBD, write the specific position of the moving point P and the corresponding conclusion, and choose a conclusion to prove it. Please draw your own picture.
(1) Proof: 1 Part lies between two parallel lines. Pass p for PQ∑AC, pass AB for q,
Then ∠APQ=∠PAC, ∠BPQ=∠PBD,
∴∠APB=∠APQ+∠BPQ=∠PAC+∠PBD.
(2) The second part is also between two parallel lines, and ∴∠APB=∠PAC+∠PBD holds.
(3) The third part is on the outer side of two parallel lines near AC. If PB passes through AC to E, then
∠PBD=∠PEC=∠PAC+∠APB or 180-(∠ PAC+∠ APB).