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It is known that, as shown in the figure, D is a point inside △ ABC connecting BD and ad, with BC as the edge, outside △ ABC, make ﹥ CBE = ﹥ abd, ﹥ BCE = ﹥ bad, be and CE cross to e, connecting de. (1) verification: bcab = bebd; (2) verification: ﹥ DBE ﹥ ABC
It is proved that: (1) in △ CBE and △ abd, ∵ - CBE = ∵ abd, ∵ BCE = ∵ bad, (1 point) ∵ - CBE ∵ abd. (2 points) ∵ bcab = bebd. (3 points) ∵ bcbe = abbd. (4 points), that is, bcab = bebd; (2) from (1) we can know that bcab = bebd, ∵ - CBE = ∵ abd, ∵ CBE + ∵ DBC = ∵ abd + ∵ DBC. (5 points), that is, ∵ DBE = ∵ ABC. (6 points) ∵ DBE ∵ ABC. (7 points)
RELATED INFORMATIONS
- 1. As shown in the figure, D is a point inside the triangle ABC, connecting BD and ad, taking BC as the edge, making an angle outside the triangle ABC, CBE = angle abd, BCE = angle bad, be, CE intersecting at point E, connecting de. prove that the triangle DBE is similar to the triangle ABC
- 2. As shown in the figure △ ABC, ad ⊥ BC, be ⊥ AC, BF = AC, if ∠ EBC = 25 °, then ∠ ACF=______ ．
- 3. As shown in the figure △ ABC, ∠ BAC = 90 & ordm;, ad ⊥ BC, ∠ Abe = ∠ EBC, EF ⊥ BC, FM ⊥ AC, DF = FM
- 4. As shown in the figure, ad and be are the heights of BC and AC respectively in ABC
- 5. In triangle ABC, ad is perpendicular to BC and D, be is the middle line, and the angle EBC is 30 degrees
- 6. As shown in the figure, D is a point on side AC of triangle ABC, CD = 2ad, AE is perpendicular to BC and E, if BD = 8, Tan angle abd = 3 / 4, find the length of AC
- 7. As shown in the figure, make equilateral triangles △ abd, △ EBC, △ fac on the same side of BC with the three sides of △ ABC respectively, and prove that the quadrilateral ADEF is a parallelogram
- 8. As shown in the figure, BD is divided into two parts, be is divided into ABC 2:5, DBE = 21 ° and the degree of ABC is calculated
- 9. As shown in the figure, BD is divided into two parts, be is divided into ABC 2:5, DBE = 21 ° and the degree of ABC is calculated
- 10. As shown in the figure, BD is divided into two parts, be is divided into ABC 2:5, DBE = 21 ° and the degree of ABC is calculated
- 11. As shown in the figure, in △ ABC, point E is on AB, point D is on BC, BD = be, ∠ bad = ∠ BCE, ad and CE intersect at point F. try to judge the shape of △ AFC and explain the reason
- 12. In the triangle ABC, ab = AC, BD = DC, take any point E in ad to judge the relationship between be and EC
- 13. As shown in the figure, in the linear triangle ABC, ∠ C = 90 °, BD is the angular bisector of △ ABC, be is the angular bisector of △ BDA, DF is the height of △ BDE
- 14. The two right sides of a right triangle are 60cm and 80cm respectively
- 15. The two right sides of a right triangle are 60cm and 80cm respectively. How many square centimeters is its area? The hypotenuse of this triangle is 100cm long. How high is the hypotenuse?
- 16. The lengths of the two right sides of a right triangle are 60cm and 80cm respectively. Find the perimeter of the right triangle and the height on the hypotenuse,
- 17. The lengths of the two right sides of a right triangle are 60cm and 80cm respectively. Find the perimeter of the right triangle and the height on the hypotenuse
- 18. The perimeter of a right triangle is 60cm, the shortest side is 15cm, and the largest side is 15cm Second, given that the sum of the two right sides of a right triangle is 34 cm, and the difference between the two right sides is 14 cm, what is the area of the triangle?
- 19. The hypotenuse of a right triangle is 100cm, one is 60cm, and the other is 80cm. How high is the hypotenuse? Because I am only a primary school student.
- 20. The three sides of a right triangle are 3cm 4cm 5cm. The area of the triangle is the square of () cm, and the height of the hypotenuse is () cm?