As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E
It is proved that: ∵ de ⊥ AB, ∵ AED = 90 ° = ∠ ACB, and ∵ ad bisecting ∵ BAC, ∵ DAE = ∠ DAC, ∵ ad = ad, ≌ ACD, ≌ AE = AC, ∵ ad bisecting ≁ BAC, ≁ ad ⊥ CE, that is, the straight line ad is the vertical bisector of the line CE
RELATED INFORMATIONS
- 1. As shown in the figure, ∠ ACB = 90 ° in △ ABC, ad bisects ∠ BAC, de ⊥ AB in E
- 2. 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.
- 3. 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
- 4. 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
- 5. 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
- 6. 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;
- 7. 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
- 8. 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
- 9. 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.
- 10. 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.
- 11. 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
- 12. 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
- 13. As shown in the figure: in △ ABC, BC = 5, extend BC to point D, so that ∠ DAC = ∠ B, ad = 6, then CD=______ .
- 14. 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
- 15. 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
- 16. In △ ABC, ∠ BAC = 90 °, BD bisection ∠ ABC, AE ⊥ BC in E. verification: AF = ad
- 17. As shown in the figure: in △ ABC, ∠ B = 90 °, ab = BD, ad = CD, calculate the degree of ∠ CAD
- 18. In △ ABC, ab = AC, ad is the midline on the side of BC, if AB = 17, BC = 16, then ad =?
- 19. In the triangle ABC, AB equals 20, AC equals 12, D is the middle line, and ad equals 8, find the length of BC
- 20. In the triangle ABC, ad is the middle line on the side of BC, AB is equal to 6, ad is equal to 5, AC is equal to 8 It's urgent!