As shown in the figure, point b.e.c.f is on the same straight line, be is equal to CF, AB is parallel to de, angle a is equal to angle D, proving that triangle ABC is equal to triangle def

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• 1. It is known that ab = AC = 5BC = 6 and ABC is equal to def The triangle def and the triangle ABC are overlapped together, and the triangle ABC does not move. The triangle def moves and satisfies that the point e moves along the direction B to C on the BC and always passes through the point a, and the EF and AC intersect at the point M. when am is the shortest time, the area of the overlapping part can be calculated? (2012 Yibin senior high school entrance examination)
• 2. As shown in the figure, four points a, F, C and D are on a straight line, AF = CD, ab ‖ De, and ab = De
• 3. Among the following conditions, () A. AB=DE，∠B=∠E，∠C=∠FB. AC=DF，AB=DE，∠C=∠DC. AB=EF，∠A=∠E，∠B=∠FD. ∠A=∠F，∠B=∠E，AC=DF
• 4. As shown in the figure, two congruent triangles ABC and def are overlapped. Fix the triangle ABC and do the following operation for the triangle def The triangle def moves to the right along the line AB (that is, point d moves in the line AB). When point d moves to the midpoint of AB, what is the shape of the quadrilateral cdbf? Explain the reason
• 5. Among the following conditions, () A. AB=DE，∠B=∠E，∠C=∠FB. AC=DF，AB=DE，∠C=∠DC. AB=EF，∠A=∠E，∠B=∠FD. ∠A=∠F，∠B=∠E，AC=DF
• 6. In the following conditions, it can be judged that △ ABC and △ def are congruent () A. The girth of AB = De, BC = EF, BC = EF, a = DC, a = D, C = f, AC = EFD, ab = De, BC = EF, and the girth of △ ABC = the girth of △ def
• 7. Under the following conditions, it is impossible to determine the congruence of △ ABC and △ def_ A.∠B=∠E=90°,AB=DE,AC=DF B.∠B=∠E=90°,∠A=∠D,AC=DF C.∠B=∠E=90°,∠C=∠F,AB=EF D.∠B=∠E=90°,AB=DE,BC=EF
• 8. Ad and be are the heights of the triangle ABC. The two heights intersect at a point h. If BH and AC are equal in length, the angle BCH =? Degree
• 9. In the triangle ABC, the angle ABC is 45 degrees. H is the intersection point of high AD and be. BH = AC, BH is perpendicular to AC
• 10. As shown in the figure: in △ ABC, ad ⊥ BC is in D, be ⊥ AC is in E, ad and be intersect in H and BH = AC, find the degree of ∠ HCD
• 11. In triangle ABC, angle A: angle B: angle c, and triangle ABC ≌ triangle def, then angle E=
• 12. In triangle ABC, if angle A: angle c: angle B = 4:3:2 and triangle ABC is equal to triangle def, then angle e is equal to
• 13. In triangle ABC and triangle def, is angle a = angle d = 70 degrees, angle B = 60 degrees, and angle e = 50 degrees similar? Why?
• 14. If triangle ABC is similar to triangle def, angle a is equal to angle e is equal to 30 degrees, and angle B is equal to 70 degrees, what is angle f equal to?
• 15. In triangle ABC and triangle def, angle a = angle d = 65 degrees, AB / AC = ed / DF, are these two triangles similar? Why?
• 16. If BC = 3, DF = 4, ∠ f = 90 °, then ∠ C =?, s triangle def =?
• 17. Junior high school triangles are similar to triangles ABC and def. If AB is equal to ab + de and AC is equal to AC + DF, is that ab Triangle similarity in junior high school Triangle ABC and triangle def, if AB than AB + de equals AC than AC + DF, is ab than de equal to AC than DF? Why? If the angle BAC equals the angle EDF, are the two triangles similar? Why?
• 18. Sina ^ 2 / SINB ^ 2 + cosa ^ 2 * COSC ^ 2 = 1, Tana ^ 2 * cotb ^ 2 = sinc ^ 2 Trigonometric ratio just contact. Seek detailed proof All right, we must add more
• 19. In △ ABC, C-A = π / 2, SINB = 1 / 3, find the value of sina 2. Let AC = √ 6, find the area of △ ABC
• 20. In RT triangle ABC, ∠ C = 90 °, ab = 2, radical 2, BC = radical 6, solve this right triangle