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

Proof: because the equilateral triangle ABC, BD = CE, ∠ ABC = ∠ ACB, △ abd ≡ BCE; ∠ BDA = ∠ BEC, ∠ FBD = ∠ bad, ∵ sum of internal angles of triangle = 180 °, ∠ BFD = ∠ abd, ∵ BDF is similar to △ BEC, ∠ BFD = ∠ BCE = 60 ° = ∠ AFE (equal to vertex angle)

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1. 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
2. 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;
3. 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
4. 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
5. 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.
6. 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.
7. 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
8. As shown in the figure, in △ ABC, be bisects ∠ ABC, de ‖ BC, ∠ Abe = 35 °, then ∠ DEB=______ Degree, ∠ ade=______ Degree
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13. As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E
14. As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E
15. It is known that: as shown in the figure, in the triangle ABC, ad is the bisector of ∠ BAC, and the extension line of intersection Ba of CE ‖ ad through point C is at E
16. As shown in the triangle ABC, ad is perpendicular to D under the following conditions: (1) angle B + angle DAC = 90 degrees, (2) angle B = angle DAC, (3) CD of ad = AC of AB, (4) The square of AB = BD times BC, where it is certain to determine that the triangle ABC is a right triangle, there are choices a, 1 B, 2 C, 3 D, 4
17. As shown in the figure: in △ ABC, BC = 5, extend BC to point D, so that ∠ DAC = ∠ B, ad = 6, then CD=______ ．
18. As shown in the figure, ad = 2, AC = 4, BC = 6, ∠ B = 36 °, ∠ d = 117 °, △ ABC ∽ DAC. (1) find the length of AB; (2) find the length of CD; (3) find the size of ∠ bad
19. As shown in Figure 10, AD / / BC, ad = 5 cm, the area of triangle abd is 10 square cm, what is the height of ad side of triangle ACD
20. In △ ABC, ∠ BAC = 90 °, BD bisection ∠ ABC, AE ⊥ BC in E. verification: AF = ad