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As shown in the figure, ∠ a = ∠ B, CE ‖ Da, CE intersects AB with E
It is proved that ∵ CE ∥ Da, ∵ a = ∵ CEB. And ∵ a = ∵ B, ∵ CEB = ∵ B. ∵ CE = CB. ∵ CEB is isosceles triangle
As shown in the figure, ∠ a = ∠ B, CE ‖ Da, CE intersects AB with E
It is proved that ∵ CE ∥ Da, ∵ a = ∵ CEB. And ∵ a = ∵ B, ∵ CEB = ∵ B. ∵ CE = CB. ∵ CEB is isosceles triangle
Known: as shown in the figure, Da ⊥ AC, EC ⊥ Ca, point B on AC, DB ⊥ be, ab = CE
It is proved that: if ∵ Da ⊥ AC, EC ⊥ Ca ≁ a = ≁ C = 90 °, e + ≁ CBE = 90 ° DB ⊥ be ≁ DBE = 90 ° then abd + ⊥ CBE = 90 °, abd = ≌ e, in △ abd and △ CEB ≌ a = ≌ C (proved) ∠ abd = ≌ e (proved) AB = Ce (known) ≌ abd ≌ CEB (ASA)
&As shown in the figure, ∠ a = ∠ B = 60 ° CE ‖ Da, CE intersects AB with E
It is proved that: ∵ a = 60 °, CE ∥ Da, ∵ CEB = 60 °, ∵ a = ∵ B = 60 °, ∵ CEB = ∵ B = ∥ ECB = 60 ° and ∫ CEB is an equilateral triangle
RELATED INFORMATIONS
- 1. As shown in the figure, in square ABCD, G is any point on BC, AE is vertical DG, CF is vertical Gd, and the perpendicular feet are e and f respectively
- 2. The area of parallelogram abed and AFCD are both 30 square centimeters. AF is perpendicular to ED, Ao, OD and ad, which are 3 cm, 4 cm and 5 cm respectively. Calculate the area and perimeter of triangle OEF
- 3. As shown in the figure, D and F are on the edge of AB of △ ABC, and ad = BF, de ‖ FG ‖ BC. De and FG intersect AC at points E and g respectively
- 4. As shown in the figure, △ ABC is an equilateral triangle, P is a point on the bisector BD of ∠ ABC, PE ⊥ AB is at point E, the vertical bisector of line BP intersects BC at point F, and the perpendicular foot is point Q. if BF = 2, the length of PE is () A. 2B. 23C. 3D. 3
- 5. What can be made of two identical triangles?
- 6. Two identical triangles can be combined into one () A. Parallelogram B. trapezoid C. rectangle
- 7. D point on AB, ad: ab = 1:3, e point on BC, be: BC = 1:4, f point on Ca, CF: CA = 1:5, s △ def = 19, find s △ ABC?
- 8. If △ ABC ∽ def, ab = 2, BC = 2 times radical 3, de = radical 2, then EF is emergency
- 9. In the triangle ABC, angle c equals 90 degrees. If angle a equals 45 degrees and C equals 2, find a and B
- 10. As shown in the figure, in the isosceles trapezoid ABCD, ab ∥ CD, DC = ad = BC, and the diagonal AC is perpendicular to the waist BC, calculate the degree of each internal angle of the trapezoid
- 11. On BC of triangle ABC, take two points D and e to make BD = CE. Observe the size relationship between ab + AC and AD + AE, and explain the reason
- 12. In triangle ABC, ad bisectors BAC and CE are perpendicular to point O and intersect AB at point E. try to explain the relationship between de and DC and explain the reason
- 13. In ABC,
- 14. In the triangle ABC, BD and CE divide ⊥ ABC, ⊥ ACB, AF ⊥ BD in F and Ag ⊥ CE in G equally. If AB = 6, BC = 12 and AC = 10, find the length of FG Such as the title It's urgent
- 15. Point G is the intersection of the three middle lines of triangle ABC, Ag is perpendicular to GC, AC is equal to 4, and BG is obtained
- 16. Let G be the center of gravity of △ ABC, Ag = 6, BG = 8, CG = 10, then the area of triangle is () A. 58B. 66C. 72D. 84
- 17. In the triangle ABC, the angle BAC = 100 degrees, de and FG bisect AB and AC vertically and intersect BC at e and G, respectively
- 18. As shown in the figure, ad is perpendicular to D, eg is perpendicular to g, angle e is equal to angle 3, and angle 1 is equal to angle 2
- 19. As shown in the figure, in △ ABC, ∠ C = 90 °, AC = BC, Da bisects ∠ cab and intersects BC at point D. can we determine a point E on AB so that the perimeter of △ BDE equals the length of AB? If yes, please point E and give proof; if not, please explain the reason
- 20. As shown in the figure, point I is the inner part of triangle ABC, AI intersects BC at point E, and intersection triangle ABC circumscribes circle at point D. prove (1dB = di (2id square = de * ad)