![](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>)
In the triangle ABC, the angle BAC = 90 degrees, ab = AC = 6cm, point G is the center of gravity of the triangle ABC, making GD / / CB intersection AB with D, connecting AG, then s triangle GAD = multiple
Point G is the center of gravity of triangle ABC and the intersection of the three midlines
When extending the intersection of Ag and BC with D, Ag: DG = 2:1
S△ABC=18
S△ABD=9
S△ADG：S△ABD=4：9
S△ADG=4
In rtabc, angle BAC = 90 degrees, angle B = 30 degrees, ab = 3, change sign 3, G is the center of gravity of ABC, Gd is parallel to BC, and the area of triangle AGD is calculated
Let AC = x, then BC = 2x. From the Pythagorean theorem in RT △ ABC, we get BC & sup2; = AB & sup2; + AC & sup2; that is, (2x) & sup2; = (3 √ 3) & sup2; + X & sup2;, then x = 3, then AC = 3, BC = 6. Let the extension line of Ag intersect BC in E, then AE = 1 / 2BC = 3 ∵ G is the weight of △ ABC
Ad is the center line of the triangle ABC, G is the center of gravity of the triangle ABC, De is parallel to AB, BC is parallel to E,
GF is parallel to AC and BC is parallel to F. if the perimeter of C triangle GEF is p and the area is Q, find the perimeter and area of triangle ABC
There is a problem with the title: it should be "Ge parallel to AB, BC to e" ∵ G is the center of gravity of the triangle ABC ∵ Ag = 2Gd, that is, Gd / ad = 1 / 3 ∵ Ge / / AB ∵ Ge / AB = GD / ad = 1 / 3, ∵ EGD = ∵ bad. Similarly, Gd / AC = GD / ad = 1 / 3, ∵ FGD = ∵ CAD ∵ BAC = ∵ EGF, so △ BAC ≈ △ EGFs △ BAC / s △ EGF = ad / Gd = 3
Ad is the center line of △ ABC, G is the center of gravity, GE ‖ AB, given s △ GDE = 2, find; s △ ABC
Because G is the center of gravity of △ ABC, then DG: Da = 1:3, and Ge / / AB, then:
S △ DAB: s △ GDE = 1:9, because s △ GDE = 2
So, s △ DAB = 18
In addition, if s △ ABC = 2S △ DAB, then s △ ABC = 36
RELATED INFORMATIONS
- 1. As shown in the figure, point G is the center of gravity of triangle ABC, Ge is parallel to AB, GF is parallel to AC Proof: GD is the middle line on the edge EF of the triangle GEF
- 2. As shown in the figure, there are two slides of the same length. The height AC of the left slide is equal to the length DF of the right slide in the horizontal direction. The relationship between the inclination angles ∠ ABC and ∠ DFE of the two slides is () A. ∠ABC=∠DFEB. ∠ABC＞∠DFEC. ∠ABC＜∠DFED. ∠ABC+∠DFE=90°
- 3. As shown in the figure, in △ ABC, D, e and F are the points on AB, AC and BC respectively, and de ‖ BC, EF ‖ AB, ad: DB = 2:3, BC = 20cm, the length of BF can be obtained
- 4. As shown in the figure, the inscribed circle I of equilateral triangle ABC is tangent to each side and the point def, the radius of the inscribed circle is 1, and the side length of the triangle is calculated There is no picture. I'm sorry. I'll make do with it,
- 5. In the triangle ABC, the angle ACB is 90 degrees, and D is the intersection of the bisectors of the three interior angles of the triangle ABC. If AC = 3, BC = 4, find the distance from D to ab?
- 6. In the triangle ABC, ∠ a > 90 °, BD and CE are the heights of the triangle respectively, and M is the midpoint of the edge BC, connecting de and DM, (1) complete the drawing according to the above requirements (2) To prove that △ MDE is an isosceles triangle (3) try to explore whether △ MDE can be a right triangle? If yes, please tell us the degree of ∠ BAC
- 7. M is the middle point of the side BC of the triangle ABC, and AB, AC are taken as the square ACDE and abgf to prove am = half EF
- 8. As shown in the figure, take sides AC and BC of △ ABC as one side respectively, and make square ACDE and cbfg outside △ ABC. Point P is the midpoint of EF. Prove that the distance from point P to AB is half of ab
- 9. Ad is the median line of △ ABC, EF is the median line of △ ABC, then the quantitative relationship between EF and ad is__________ .
- 10. Fold rectangle ABCD along AE so that point B falls on median line FG of right angled trapezoid AECD, and ab = root 5, then what is the length of AE? (trapezoid in rectangle) AE is trapezoidal bevel (waist)
- 11. In the arcuate ABC, ad = BD, AE = EC, the area of triangle ABC is equal to 120 square centimeter
- 12. As shown in the figure, D and E are two points on the edge BC of △ ABC, and BD = EC. Prove: ab + AC = AD + AE
- 13. Let the image of function y = f (x) (x ∈ R) be symmetric with respect to line x = 0 and line x = 1, and if x ∈ [0,1], f (x) = X2, then f (− 32)=______ ．
- 14. If the image of function f (x) = (1-ax) / (1 + ax) (x is not equal to 1 / a) is symmetric with respect to y = x, then what is a?
- 15. Given the function f (x) = x ^ 3 + ax * x-x + 2, if f (x) is a decreasing function on (0,1), then the maximum value of A
- 16. When x ∈ [0,2], the function f (x) = ax ^ 2 + 4 (A-1) x-3 gets the maximum value when x = 2, then the value range of A
- 17. Given that f (x) = x ^ 3-2x ^ 2 + X-2, if the extremum of function g (x) = f (x) + (1 / 3) MX exists, then the value range of real number m is?
- 18. Find the maximum and minimum of the function f (x) = x squared by e to the - x power
- 19. The distance from the moving point to the point (1,0) is equal to the distance from the moving point to the straight line y + 2 = 0
- 20. The distance from the point on the curve m to the point F (1,0) is smaller than the distance from it to the straight line L: x + 2 = 0,