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

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• 1. 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
• 2. In triangle ABC, ad is the middle line, AE is the middle line of triangle abd, and angle bad = angle BDA
• 3. 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
• 4. 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
• 5. 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;  
• 6. 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
• 7. 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
• 8. 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
• 9. 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&
• 10. 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
• 11. In the triangle ABC, the extension of AB: AC = 3:5, BD = CE, de intersects the extension of BC at point F. if DF = 15, find the length of EF
• 12. It is known that in the triangle ABC, ab = AC, D point is on AB, e point is on the extension line of AC, and BD = CE, connecting de with BC at f point No picture
• 13. In triangle ABC, ad bisects BC, De is the angle bisector of angle ADC, DF is the angle bisector of angle ADB
• 14. If AB = 10, eg = 3, then Ag =?
• 15. In △ ABC, eg is a point on AB, AE = BG, ed ∥ AC, FG ∥ BC to prove DF ∥ ab
• 16. As shown in the figure, △ ABC, ad is the angular bisector, e and F are the points on AC and ab respectively, and ∠ AED + ∠ AFD = 180 °. What is the relationship between de and DF, and explain the reason
• 17. As shown in the figure, in the triangle ABC, ad bisects ∠ BAC, BC intersects D, e and F are the points on AB and AC respectively. If the angle AED + ∠ AFD = 180 °, then de = DF
• 18. As shown in the figure, △ ABC, ad is the angular bisector, e and F are the points on AC and ab respectively, and ∠ AED + ∠ AFD = 180 °. What is the relationship between de and DF, and explain the reason
• 19. In △ ABC, ab = AC, D is the point on BC, DF ⊥ AC is on fed ⊥ BC is on D, if ∠ AED = 150 °, calculate the degree of ∠ EDF?
• 20. In the triangle ABC, the angle ACB is equal to 90 degrees, the points E and F are on the edge AB, and the angle CEB = angle ECB, the angle CFA = angle FCA, and the degree of the angle ECF is calculated