歷屆試題講解---**Question Stem:**
20. 圖 (十三) 為一張五邊形紙片 ABCDE，F 點在 $\overline{CD}$ 上，且以 $\overline{BE}$、$\overline{BF}$、$\overline{FE}$ 為摺線將紙片向內摺至同一平面後，A、C、D 恰重疊在同一點 P，如圖 (十四) 所示。若 $\overline{BE} > \overline{FE} > \overline{BF}$，則根據圖 (十四) 中標示的角，判斷下列敘述何者正確？
**Translation of Question Stem:**
20. Figure (13) shows a pentagonal piece of paper ABCDE, with point F on $\overline{CD}$. After folding the paper inwards along the fold lines $\overline{BE}$, $\overline{BF}$, and $\overline{FE}$ so that points A, C, and D coincide at the same point P, as shown in Figure (14). If $\overline{BE} > \overline{FE} > \overline{BF}$, determine which of the following statements is correct based on the angles marked in Figure (14).
**Image Description:**
* **Image 1: 圖 (十三) [Figure (13)]**
* Type: Geometric figure (Pentagon).
* Main Elements:
* A pentagon labeled ABCDE.
* Points A, B, C, D, E are the vertices.
* Point F is on the side CD.
* Lines: Solid lines form the perimeter segments BC, CD, DE, EA. Dashed lines represent BE, BF, FE, which are indicated as fold lines.
* Arrows: Curved arrows are shown inside the pentagon, indicating that parts of the pentagon are folded inwards towards the center. One arrow points from the region near A towards the center, and two arrows point from the regions near C and D towards the center/region near F.
* Title: 圖 (十三) [Figure (13)]
* **Image 2: 圖 (十四) [Figure (14)]**
* Type: Geometric figure (Polygon with internal lines).
* Main Elements:
* Represents the folded state of Figure (13).
* The vertices B and E of the original pentagon are still visible.
* The original points A, C, and D have been folded to coincide at point P, located inside the region BFE.
* Lines: Solid lines form the segments BE, BF, FE. Solid lines also connect P to B, F, and E (forming triangles PBE, PBF, PFE).
* Angles: Angles around point F are labeled as angle 3 and angle 4. Angles around point B are labeled as angle 1 and angle 2. Angles around point E are labeled as angle 5 and angle 6. Angle 1 is $\angle PBE$. Angle 2 is $\angle PBF$. Angle 3 is $\angle BFP$. Angle 4 is $\angle EFP$. Angle 5 is $\angle EFP$. (Correction: Angle 5 is $\angle PEF$, and angle 6 is $\angle PEB$).
* Dashed lines represent the original edges of the pentagon that are now folded underneath or form the outer boundary of the unfolded parts (parts of BC, CD, DE, EA).
* Title: 圖 (十四) [Figure (14)]
**Given Condition:**
$\overline{BE} > \overline{FE} > \overline{BF}$
**Options:**
(A) $\angle 3 + \angle 4 = 90^\circ$, $\angle 1 + \angle 2 > \angle 5 + \angle 6$
(B) $\angle 3 + \angle 4 = 90^\circ$, $\angle 1 + \angle 2 < \angle 5 + \angle 6$
(C) $\angle 3 + \angle 4 \neq 90^\circ$, $\angle 1 + \angle 2 > \angle 5 + \angle 6$
(D) $\angle 3 + \angle 4 \neq 90^\circ$, $\angle 1 + \angle 2 < \angle 5 + \angle 6$