In the known triangle ABC, the angle B = 90 °, ab = 3, BC = 4, G is the center of gravity, and the value of BG is obtained

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• 1. D is the midpoint of BC, AE is equal to one third of AC, if the area of triangle ade is equal to 4, calculate the area of triangle ABC
• 2. Given that the triangle ABC is an equilateral triangle, take points E and F on AC and BC respectively, and AE = CF, be and AF intersect at point D, then ∠ BDF = what The next two questions of this question, the last question of Changjun bilingual mathematics school-based similar triangle judgment 4
• 3. E. F is two points on the edge BC of triangle ABC, and be = CF, connecting AE and AF. proof: ab + AC is greater than AE + AF
• 4. It is known that on the BC side of the triangle ABC, be = CF is cut to connect AE AF, which means that ab + AC is greater than AE + AF
• 5. As shown in the figure, in △ ABC, ∠ C = 90 °, a = 30 ° and ab + BC = 12cm, then the length of the hypotenuse AB is______ cm．
• 6. If be: EC = 3:2, AB: EC = 4:1, then AE: AC: BC =?
• 7. As shown in the figure, in △ ABC, a = 30 °, B = 45 °, D is on AB, e is on AC, and AE = EC = De, then ad2: BC2 is equal to______ ．
• 8. On Pythagorean theorem The teacher asked the students to go home and prepare a 21cm long wooden stick for use in class. In order to prevent the stick from breaking, Xiao Ming wanted to put it into his pencil case. It is known that Xiao Ming's pencil case is a cuboid 20cm long and 8cm wide. Can the stick prepared by Xiao Ming be put into his pencil case? Note: write down the steps
• 9. It is known that the sum of the two right sides of a right triangle is 5 cm and the hypotenuse is 2 cm, then the area of the right triangle is 2 cm____ .
• 10. If the three sides of a right triangle are A-B, a, a + B and both a and B are positive integers, the length of one side of the triangle may be () A. 61B. 71C. 81D. 91
• 11. Difficult math problem: triangle ABC, angle c = 90 degrees, angle a = 30 degrees, triangle C point does not move, rotates counterclockwise, edge AC intersects AB at f point, Triangle ABC, angle c = 90 degrees, angle a = 30 degrees, triangle C point does not move, rotates counter clockwise, edge AC (CD side after rotation) intersects AB at f point, triangle after rotation is CDE. Rotation angle is ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0&
• 12. As shown in the figure, in △ ABC, BD bisects ∠ ABC intersection AC at D, CE bisects ∠ ACB intersection AB at e, CE and BD intersection F, connects AF and extends intersection BC at h, FG ⊥ BC at g through F. (1) if ∠ ABC = 45 ° and ∠ ACB = 65 °, calculate the degree of ∠ HFG; (2) according to the law in (1), explore the relationship between ∠ ABC, ∠ ACB and ∠ HFG; (3) try to explore the size relationship between ∠ BFH and ∠ CFG, and explain the reason
• 13. As shown in the figure, in the triangle ABC, angle a = 60 °, BD and CE bisect angle ABC and angle ACB respectively, BD and CE intersect at point O, try to judge the quantitative relationship of be, CD and BC and prove it
• 14. As shown in the figure, in the triangle ABC, ad and AE are the height and the middle line on the edge of BC respectively. AB = 9, AC = 7, BC = 8, find the length of CD, de and AE
• 15. As shown in the figure, in the triangle ABC, ab = AC, take a point E on AC, take a point D on the extension line of Ba, make ad = AE, connect de and extend BC to F Whether or not it is still true to exchange the condition "ad = AE" and the conclusion "DF 8869; BC" and whether or not it is still true to exchange the condition "ad = AE" and the conclusion "DF BC" and whether or not it is still true to test the test of the test of the test of the test of the test of the test of the test of the test of the test of the test of the test of the test of the test of whether it is still true to exchange the condition "ad = AE" and the conclusion "DF BC" BC "and the condition" DF BC "and whether the condition of the condition of the condition" ad = AE "and the condition" DF BC "and whether the condition" and whether it is the condition of the exchange, whether it is the exchange, whether the condition of the condition of the condition of the condition of the exchange of the condition "and the exchange of the exchange of the exchange of the exchange of the condition" the& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp;  
• 16. In the triangle ABC, the angle BAC = 90 ° AB = AC, take a point D in the triangle, make the angle abd = 30 ° and BD = Ba, AE perpendicular to E. prove the bisection of AD
• 17. It is known that ad is the middle line of △ ABC, AE is the middle line of △ abd, ab = DC, ∠ bad = ∠ BDA I'm going to hand it in in the evening. Can anyone answer this question? It's not easy to draw pictures. You can draw by yourself. I only learned congruent triangles and axisymmetry. Please use my knowledge to solve it
• 18. In triangle ABC, ad is the middle line, AE is the middle line of triangle abd, and angle bad = angle BDA
• 19. In the triangle ABC, ab = AC, D is the point on AB, e is the point on the extension line of AC, and BD = CE, de intersects BC in flight. The proof: DF = Fe
• 20. It is known that in △ ABC, ab = AC, the straight line DF intersects AB at point D, BC at point E, and the extension line of AC intersects at point F, BD = CF