![](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>)
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
Extend AG to G ', and intersect BC at D, so that DG = DG', then △ BDG ≌ △ CDG ′, ≌ CG ′ = BG = 8, ∵ DG = 12ag = 3, ∵ DG = DG ′ = 3, ∵ GG ′ = 6, ∵ CG = 10, ≌ CGG ′ is a right triangle, ≌ s △ GBC = s △ CGG ′ = 12 × 8 × 6 = 24, ≌ s △ ABC = 3S △ GBC = 72
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
Extend AG to G ', and intersect BC at D, so that DG = DG', then △ BDG ≌ △ CDG ′, ≌ CG ′ = BG = 8, ∵ DG = 12ag = 3, ∵ DG = DG ′ = 3, ∵ GG ′ = 6, ∵ CG = 10, ≌ CGG ′ is a right triangle, ≌ s △ GBC = s △ CGG ′ = 12 × 8 × 6 = 24, ≌ s △ ABC = 3S △ GBC = 72
As shown in the figure, let m be the center of gravity of △ ABC, and am = 3, BM = 4, CM = 5, then the area of △ ABC is______ ．
Extend BM to AC at point D, and then extend BD to e, so that de = DM, connect CE, ∵ m is the center of gravity of △ ABC, ∵ ad = CD, MD = 12bm, ∵ ADM = ≌ CDE (equal to vertex angle), de = DM, ≌ AMD ≌ CDE (SAS), ≌ am = EC = 3,
RELATED INFORMATIONS
- 1. 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
- 2. 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
- 3. In ABC,
- 4. 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
- 5. 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
- 6. As shown in the figure, ∠ a = ∠ B, CE ‖ Da, CE intersects AB with E
- 7. 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
- 8. 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
- 9. 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
- 10. 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
- 11. 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
- 12. 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
- 13. 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
- 14. 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)
- 15. As shown in the figure, point I is the heart of △ ABC, the extension line of AI intersects with BC at point D, and intersects with the circumscribed circle of △ ABC at point E. verify EB = EC = EI
- 16. In △ ABC, the angular bisectors AE and be of ∠ BAC and ∠ ABC intersect at point E, extend the circumscribed circle of AE intersecting △ ABC at point D, connect BD, CD and CE, and ∠ BDA = 60 ° ① prove that △ BDE is an equilateral triangle; ② guess what kind of quadrilateral bdce is if ∠ BDC = 120 ° and prove your guess; ③ under the condition of ②, when CE = 4, calculate the area of quadrilateral abdc
- 17. (1) if EF = 5cm, then AB = --- (2) what's the difference between AF and de Please help··
- 18. As shown in the figure, △ ABC is an equilateral triangle, which is cut by a rectangle parallel to BC, and ab is cut into three equal parts. Then the area of the shadow part in the figure is () A. 19B. 29C. 13D. 49
- 19. In triangle ABC, ad = 3bd, be = 2ec, AF = CF
- 20. As shown in the figure, in the triangle ABC, D is a point on the edge AB, and ad = AC, De is parallel to BC, CD bisection angle EDF proves that AF bisection CD