![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Proof: as shown in Figure 9, in the triangle ABC, ab = AC,
∵AB=AC,BD=CD,
The ∧ ABC and ∧ ade are isosceles triangles
∵∠BAD=40°
∴∠DAE=40°
∴∠ADE= 12（180°-∠DAE）= 12（180°-40°）=70°
And ∵ △ ABC is an isosceles triangle
∴AD⊥CD
∴∠CDE=90°-∠ADE=90°-70°=20°．
So the answer is 20 degrees
The bisectors BP and CP of angle ABC intersect at point P. is the distance from point P to AB, BC and AC equal? Explain the reason
In a hurry
How about ABC 2 bisectors?
It should be △ ABC, right?
Of course, wait
Because BP is the bisector of ∠ ABC, the distance from point P to Ba and BC is equal
And CP is the bisector of ∠ ACB, so the distance from point P to BC and AC is equal
So the distance from point P to AB, BC and AC is equal
As shown in the figure, △ abd and △ ace are equilateral triangles, and ab
【BE=CD】
prove:
∵ abd and ace are regular triangles
∴AB=AD,AE=AC,∠BAD=∠CAE=60°
∴∠BAD+∠DAE=∠CAE+∠DAE
That is, BAE = DAC
∴△BAE≌△DAC（SAS）
∴BE=CD
RELATED INFORMATIONS
- 1. If vector AP = 1 / 3 vector Pb and vector AB = Λ vector BP, then the value of Λ is?
- 2. Point a and B are two points on O, ab = 10, point P is a moving point on O (P does not coincide with ab) to connect AP, Pb passes through point o as OE ⊥ AP, of ⊥ Pb, and point EF is (1) Find the distance from the long (2) point O of the line EF to AB, and find the radius of O
- 3. Take any two numbers P and Q (P ≠ q) from the four numbers 2, 3, 4 and 5 to form the functions y = px-2 and y = x + Q, and make the image of these two functions If the intersection point is on the right side of the straight line x = 3, how many pairs of ordinal numbers are there in total?
- 4. Triangle ABC is an equilateral triangle, PA is perpendicular to plane ABC, and D is the midpoint of BC
- 5. In equilateral triangle ABC, is de / / BC. Angle ade an equilateral triangle?
- 6. It is known that △ ABC and △ ade are equilateral triangles, and points a and E are on the same side of BC (1) As shown in Figure 1, if point D is on BC, write the quantitative relationship among line segments AC, CD and CE, and prove it; (2) as shown in Figure 2, if point D is on the extension line of BC, and other conditions remain unchanged, directly write the quantitative relationship among AC, CD and CE
- 7. As shown in the figure, D in △ ABC is any point on edge BC, de and DF are bisectors of △ ADB and △ ADC respectively, connecting EF. Try to judge the shape of △ def and explain the reason
- 8. In the triangle ABC, the angle BAC = 90 ° AB = AC, take a point D in the triangle to make the angle abd = 30 ° and BD = Ba, AE perpendicular to BD and e to find the bisector angle EAC of AD
- 9. As shown in the figure, in the triangle ABC, the angle ABC is 90 degrees and the angle c is 30 degrees. Rotate the triangle ABC counterclockwise around point a to the position of triangle ab'c ', and point B falls on AC The value of tancdb 'is?
- 10. In RT △ ABC, ∠ C = 90 degree, ∠ a = 30 degree, then BC: AC: ab = what
- 11. As shown in the figure, in △ ABC, ∠ a = 36 °, ABC = 40 °, be bisection ∠ ABC, ∠ e = 18 °, CE bisection ∠ ACD? Why?
- 12. In △ ABC, ∠ ACB = 90 ° ch ⊥ AB in H, △ ACD and △ BCE are equilateral triangles. (1) prove: △ Dah ∽ ECH; (2) if ah: HB = 1:4, find s △ Dah: s △ ECH
- 13. It is known that, as shown in the figure, in △ ABC, the bisector of ∠ ABC and ∠ ACB intersects at point o
- 14. When the angle BAC is equal to 50, the angle BOC is equal to 50
- 15. In the triangle ABC, the angle a = 80 degrees, e, F, P are a point on the edge of AB, AC, BC respectively, be = BP, CP = CF to calculate the angle EPF
- 16. In ABC, AB is equal to AC, BF is the height on the side of AC, and the angle FBC is equal to 1 / 2 angle BAC
- 17. As shown in the figure, in △ ABC, CE and BF are two heights. If a = 70 ° and BCE = 30 °, then the degree of EBF is______ The degree of FBC is______ ．
- 18. In RT △ ABC, ∠ ACB = 90 °, ab = 5, AC = 3, D is a point on the hypotenuse AB, through point a make AE vertical CD, perpendicular foot e, AE intersection line BC at point F 1 when Tan angle BCD = half, find the length of line BF 2 when f is on the edge BC, let ad be x and BF be y, and find the functional relation of Y with respect to X 3 when BF = 5 / 4, find the length of segment ad More detailed proof!
- 19. In the triangle ABC, ab = AC, CD is the height of edge AB, and it is proved that ∠ BCD = half ∠ a
- 20. In △ ABC and △ def, angle B = angle e = 90 °, angle a = 34 °, angle d = 56 ° AC = DF, then △ ABC and △ def_____ The reason is_______