As shown in Figure 5, it is known that in the triangle ABC, AB is greater than AC, the bisector of angle B and the bisector of the outer angle of angle c intersect at D and DF, and BC intersects AB and AC at f and e respectively Question: explain BF = EF + CE.

Set point G on the extension line of BC
Known, DF ‖ BC,
It can be concluded that: ∠ FDB = ∠ CBD = ∠ FBD, ∠ EDC = ∠ GCD = ∠ ECD,
So BF = DF, CE = De,
BF = DF = EF + de = EF + CE

RELATED INFORMATIONS

1. As shown in the figure, it is known that de ∥ BC, DF and be are divided into ∥ ade and ∥ ABC equally, and it is proved that ∥ FDE = ∥ DEB
2. As shown in the figure, in △ ABC, be bisects ∠ ABC, de ‖ BC, ∠ Abe = 35 °, then ∠ DEB=______ Degree, ∠ ade=______ Degree
3. As shown in the figure, in the isosceles triangle ABC, ∠ B = 90, ab = BC = 4cm, point P moves from point a to B at the speed of 1m / s, At the same time, point Q moves from point B to point C at a speed of 2 m / s (1) Which point will arrive first? (2) Let the area of triangle ACB be Y1 and the area of triangle qAB be Y2 after X minutes (3) When the moving time is in what range: (1) the area of triangle PCB is larger than that of triangle; (2) the area of triangle PCB is smaller than that of triangle qAB? Picture too late to pass, sorry!
4. Known: as shown in the figure, in △ ABC, ab = AC, ad bisects ∠ BAC, CE ⊥ AB in E, intersects ad in F, AF = 2CD, find the degree of ∠ ace
5. As shown in the figure, the high BD and CE of △ ABC intersect at point F. (1) if ∠ abd = 36 °, calculate the degree of ∠ ace; (2) if ∠ a = 50 °, calculate the degree of ∠ BFE
6. AE bisection BAC.CE Divide ∠ ACD equally (1) if AB / / CD, judge whether △ ace is a right triangle, please explain the reason; (2) if ace is a right triangle AE bisection BAC.CE Bisecting ∠ ACD (1) If AB / / CD, judge whether △ ace is a right triangle, please explain the reason; (2) If the triangle ace is a right triangle, judge whether the line AB is parallel to the line CD, please explain the reason
7. As shown in figure a, CE / / AB, so ∠ 1 = 2 = B, so ∠ ACD = 1 + ∠ 2 = a + B, which is a useful conclusion, In the quadrilateral ABCD of figure B, do AE / / BC to intersect DC with e through A. if you have this conclusion, find the degree of ∠ a + ∠ B + ∠ C + ∠ D Figure a http://hiphotos.baidu.com/yalijudy/pic/item/099efed1bbb16a299a50274f.jpg Figure B http://hiphotos.baidu.com/yalijudy/pic/item/6750e5f54b044b34bd3109e2.jpg
8. Known: as shown in the figure, CE bisects ∠ ACD, ∠ 1 = ∠ B, verification: ab ‖ CE
9. As shown in the figure, it is known that AB / / CD, CE divide ∠ ACD equally, hand AB to e, ∠ a = 118 °, please fill in the reason for ∠ 2 = 31 °
10. In △ ABC, Sina * SINB = cos ^ 2 (C / 2), C = 4, C = 40 ° to find the value of A
11. It is known that in the triangle ABC, AB is greater than AC, the bisector of angle B intersects d with the bisector of the outer angle of angle c, DF parallels BC, and AB and AC intersect F and e respectively BF=EF+CE.
12. In the known triangle ABC, the bisector of angle ABC and the bisector of angle ACB intersect at point F, make DF \ \ BC through point F, intersect AB at point D, intersect AC at point E Then: (1) how many isosceles triangles are there? Why? (2) what is the relationship between BD, CE and de? Please prove
13. As shown in the figure △ ABC, ad is the angle bisector, AE is high ∠ B = 60 °∠ C = 40 ° to find the degree of ∠ ADB and the degree of ∠ DAE
14. It is known that D and E are the points on the sides BC and AC of equilateral △ ABC, and BD = CE, be and ad intersect at the point F;
15. D. E are the points on the sides BC and AC of equilateral △ ABC, and BD = CE, connect be = ad, they intersect at point F, find the degree of angle AFE
16. It is known that D and E are the points on the sides BC and AC of the equilateral triangle ABC, BD = CE, connect be and ad, intersect point F, and prove the angle AFE = 60 degrees
17. It is known that, as shown in the figure, in △ ABC, ∠ BAC = 90 ° ad ⊥ BC is at point D, be bisects ∠ ABC, intersects ad at point m, an bisects ∠ DAC, intersects BC at point n
18. As shown in the figure, in △ ABC, AE is the median line, ad is the angular bisector, AF is high, fill in the blanks: (1) be=______ =12______ （2）∠BAD=______ 12______ （3）∠AFB=______ =90°（4）S△ABC=______ S△ABE．
19. As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E
20. As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E