你看下图片帮我解题教程做出来给我吧，我不会做---Problem Number: 12
Points: 18
Introductory Text:
已知E,F分别是AB,CD上的动点,P也是平面内的一动点.
(Given that E, F are moving points on AB, CD respectively, and P is also a moving point in the plane.)
Sub-problem (1):
如图①,若 AB//CD,求证:∠EPF=∠BEP+∠PFD;
(As shown in Figure ①, if AB || CD, prove: ∠EPF = ∠BEP + ∠PFD;)
Sub-problem (2):
如图②,若∠EPF=∠PFD-∠BEP,求证:AB//CD;
(As shown in Figure ②, if ∠EPF = ∠PFD - ∠BEP, prove: AB || CD;)
Sub-problem (3):
如图③,AB//CD,移动点 E,F,使∠EPF=90°,∠PEG=∠PEB,试探究∠AEG与∠PFD之间的数量关系,并说明理由.
(As shown in Figure ③, AB || CD, move points E, F, such that ∠EPF = 90°, ∠PEG = ∠PEB, explore the quantitative relationship between ∠AEG and ∠PFD, and explain the reason.)
Figure Description:
Figure ①:
Type: Geometric figure.
Elements:
- Two horizontal lines labeled AB (upper) and CD (lower). The points B and A are labeled on the upper line, and D and C are labeled on the lower line.
- Point E is on line AB.
- Point F is on line CD.
- Point P is located between lines AB and CD.
- Line segment PE connects point P to point E.
- Line segment PF connects point P to point F.
- Label: ① below the figure.
Figure ②:
Type: Geometric figure.
Elements:
- Two horizontal lines. The upper line is labeled A to the right of E, and likely extends to B on the left (B is faintly visible). The lower line is labeled C to the right of F, and likely extends to D on the left (D is faintly visible). We can refer to them as parts of lines AB and CD.
- Point E is on the upper line (part of AB).
- Point F is on the lower line (part of CD).
- Point P is located above the upper line.
- Line segment PE connects point P to point E.
- Line segment PF connects point P to point F.
- Label: ② below the figure.
Figure ③:
Type: Geometric figure.
Elements:
- Two horizontal lines. The upper line is labeled A to the right of G and E, and likely extends to B on the left (B is faintly visible). The lower line is labeled C to the right of F, and likely extends to D on the left (D is faintly visible). We can refer to them as parts of lines AB and CD.
- Point E is on the upper line (part of AB).
- Point G is on the upper line (part of AB), to the right of E.
- Point F is on the lower line (part of CD).
- Point P is located between the lines AB and CD, to the left of E and F.
- Line segment PE connects point P to point E.
- Line segment PF connects point P to point F.
- Line segment PG connects point P to point G.
- An angle symbol at P in triangle PEG indicates ∠EPG is a right angle (90°).
- Label: ③ below the figure.