(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
The proof of the first question can be proved by the corner formula of the triangle, and the formulas are listed to express AC and DF with known conditions, so that AC and DF are equal; when the first question is done, it is not difficult to get the answer of the second question, and the second question is true
RELATED INFORMATIONS
- 1. 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
- 2. 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______ .
- 3. 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
- 4. 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
- 5. 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
- 6. In the triangle ABC, AE bisects the angle BAC (angle c is greater than angle b), f is the point above AE, FD is perpendicular to BC and D. try to deduce the quantitative relationship between angle EFD and angle B, angle C
- 7. In the triangle ABC, AE bisects the angle BAC, angle c > angle B, f is on the extension line of AE, FD is perpendicular to D, try to deduce the relationship between angle EFD, angle B and angle C
- 8. As shown in the figure, point G is the center of gravity of △ ABC, and de passes through points g, de ‖ BC, CEF ‖ AB, s △ ABC = 18 to calculate the area of quadrilateral bdef
- 9. The length of equilateral △ ABC side is 8, D is a moving point on AB side, passing through D as de ⊥ BC at point E, passing through e as EF ⊥ AC at point F. (1) if ad = 2, find the length of AF; (2) when ad takes what value, de = EF
- 10. As shown in the figure, in triangle ABC and triangle def, angle a = angle D, AC = DF, AE = BD. please explain why BC is parallel to ef
- 11. It is known that in △ ABC and △ def, ab = De, BC = EF, ∠ BAC = ∠ EDF = 1000;
- 12. As shown in the figure, in triangle ABC and triangle def, Ag and DH are respectively high, and ab = De, Ag = DH, ∠ BAC = ∠ EDF
- 13. 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?
- 14. 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
- 15. It is known that G is the center of gravity of the triangle ABC and O is any point in the plane
- 16. 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
- 17. 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
- 18. 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.
- 19. 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
- 20. 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