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;

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• 1. 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
• 2. 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
• 3. 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.
• 4. 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.
• 5. 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
• 6. As shown in the figure, in △ ABC, be bisects ∠ ABC, de ‖ BC, ∠ Abe = 35 °, then ∠ DEB=______ Degree, ∠ ade=______ Degree
• 7. 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!
• 8. 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
• 9. 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
• 10. 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
• 11. 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
• 12. 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
• 13. 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
• 14. 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．
• 15. As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E
• 16. As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E
• 17. 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
• 18. 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
• 19. As shown in the figure: in △ ABC, BC = 5, extend BC to point D, so that ∠ DAC = ∠ B, ad = 6, then CD=______ ．
• 20. 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