It is known that G is the center of gravity of the triangle ABC and O is any point in the plane

Vector GA = vector OA vector og vector GB = vector ob vector og vector GC = vector og vector OC
Vector GA + vector GB + vector GC = vector OA - vector og + vector ob - vector og + vector oc - vector og = 0 vector
3 vector og = vector OA + vector ob + vector PC OK

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1. The plane passes through the center of gravity of the triangle ABC, B and C are on the same side of the plane, and a is on the other side of the plane, If the distances from a, B and C to the plane are a, B and C respectively, then the relationship between a, B and C is
2. As shown in the figure, ad is the angular bisector of ∠ cab, de ‖ AB, DF ‖ AC, EF intersects ad at point O. excuse me: (1) is do the angular bisector of ∠ EDF? If so, please prove it; if not, please explain the reason. (2) if the conclusion is exchanged with any of the conditions in which ad is the angular bisector of cab, de ‖ AB, DF ‖ AC, is the proposition correct?
3. As shown in the figure, in triangle ABC and triangle def, Ag and DH are respectively high, and ab = De, Ag = DH, ∠ BAC = ∠ EDF
4. It is known that in △ ABC and △ def, ab = De, BC = EF, ∠ BAC = ∠ EDF = 1000;
5. (1) It is known that in △ ABC and △ def, ab = De, BC = EF, ∠ BAC = ∠ EDF = 100?: in △ ABC ≌ △ def (2), if the condition is changed to ab = De, BC = EF, ∠ BAC = ∠ EDF = 70?, is it still true
6. In triangle ABC and triangle def, if AB = de and angle BAC = angle EDF, the triangle ABC is congruent to triangle def, A: AC = DF B: angle ABC = angle def C: BC = EF D: angle ACB = angle DFE
7. As shown in the figure, if the vertices e, F and D of the diamond BEDF are on the edge of △ ABC, and ab = 18, AC = BC = 12, then the perimeter of the diamond is______ ．
8. Given that the triangle ABC is equal to the triangle DAF, ab = 2, AC = 4, the circumference of the triangle DEF is even, then what is the length of ef
9. In the triangle ABC, D is the midpoint of AB; AE is 2 / 3 AC; CF is 3CD; find the area ratio of EFD and ABC
10. It is known that, as shown in figure a, in △ ABC, AE bisects ∠ BAC (∠ C ＞ b), f is the upper point of AE, and FD ⊥ BC is in D. (1) try to explain: ∠ EFD = 12 (∠ C - ∠ b); (2) when F is on the extension line of AE, as shown in Figure B, other conditions remain unchanged, is the conclusion in (1) still valid? Please give reasons
11. As shown in Figure 6, in the plane rectangular coordinate system, the three vertices of △ ABC are a (m, 4) B (6,0) C (- m, - 4), and AC passes through the origin o, BH is perpendicular to AC and H Find the value of AC * BH () to get the positive solution and offer a reward of 40
12. It is known that a [0, a], [b, 0], [C, 0] are the three vertices of △ ABC. A straight line L passing through the origin o of the coordinate intersects with the line AB at point D, and is the extension of ca (1) if the angle BOD is 45 °, calculate the degree of BPD
13. As shown in the figure, make a square from the three sides of RT △ ABC. If the side length of the largest square is 8cm, then the sum of the areas of square m and square n is______ cm2．
14. As shown in the figure, in RT △ ABC, the area sum of square Adec and square bcfg is () A. 150cm2b. 200cm2c. 225cm2d. Unable to calculate
15. It is known that, as shown in the figure, in triangle ABC de / / BC, and the area of triangle ABC is equal to the area of trapezoid bced, the ratio of De to BC is calculated
16. As shown in the figure, fold a triangular piece of paper ABC along De, and point a falls inside the quadrilateral bced (1). If ∠ a = α, find ∠ 1 + 2
17. (1) As shown in the figure, the triangle ABC paper is folded along De to form figure 1. At this time, point a falls inside the quadrilateral bced, and there is a quantitative relationship between angle A and angle 1 and angle 2, which remains unchanged. Find out the quantitative relationship and explain the reason; (2) If the point a falls on be or CD, write the relationship between angle A and angle 2, angle A and angle 1, and explain the reason; (3) If folded into Figure 4, write the relationship between angle A and angle 1, angle 2, and explain the reason; (3) if folded into figure 5, write the relationship between angle A and angle 1, angle 2, and explain the reason
18. As shown in the figure, fold the △ ABC paper along de. when point a falls inside the quadrilateral bced, try to explore,
19. As shown in the figure, in △ ABC, ∠ C = 90 °, D is the point on AC, de ⊥ AB is at point E. if AB = 10, BC = 6, de = 2, calculate the area of quadrilateral DEBC
20. As shown in the figure, in △ ABC, ∠ C = 90 ° de bisects AB vertically, intersects BC with E, ab = 20, AC = 12. (1) find the length of be; (2) find the area of quadrilateral Adec