![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
As shown in the figure, △ EBD is obtained by turning the right triangle ruler ABC with 30 ° angle clockwise 150 ° around point B and connecting CD. If AB = 4cm, the area of △ BCD is () A. 43B. 23C. 3D. 2
Make a vertical line of be through point D, the perpendicular foot is f, ∵ - ABC = 30 °, ∵ Abe = 150 ° ∵ CBE = ∵ ABC + ∵ Abe = 180 °, ∵ in RT △ ABC, ab = 4, ∵ ABC = 30 °, ∵ AC = 2, BC = 23. From the nature of rotation, we can see that BD = BC = 23, de = AC = 2, be = AB = 4. From DF × be = BD × De, that is, DF × 4 = 23 × 2, we can get DF = 3, s △ BCD = 12 × BC × DF = 12 × 23 × 3 = 3cm2
RELATED INFORMATIONS
- 1. As shown in the figure, the right angle triangle plate ABC with the inclined edge length of 6cm and ∠ a = 30 ° rotates 90 ° clockwise around point C to the position of △ a ′ B ′ C, and then translates to the left along CB so that point B ′ falls on the inclined edge ab of the original triangle plate ABC. Then the distance of the triangle plate's left translation is___ cm．
- 2. A right triangle plate ABC with 12 cm long hypotenuse and 60 degree angle B is rotated 90 degrees anticlockwise around point C to the position of triangle a'b'c ', and then along CB
- 3. What is the difference between an axisymmetric figure and an axisymmetric figure
- 4. The difference between axisymmetric and axisymmetric figures
- 5. The difference between axisymmetric figure and axisymmetric figure
- 6. The difference and relationship between axisymmetric figure and two figures being axisymmetric
- 7. What are the differences and connections between axisymmetric and axisymmetric figures?
- 8. Differences and relations between axisymmetric and axisymmetric figures There are two axes of symmetry in axisymmetric figures, and the axes of symmetry in axisymmetric figures may be
- 9. What can two circles, two triangles and two parallel lines make Junior one mathematics
- 10. Please use a triangle, two parallel lines, and a semicircle Use the above graphics as components, try to conceive meaningful graphics, and add one or two appropriate, humorous commentary
- 11. As shown in the figure, the hypotenuse ab of the right angle triangle plate ABC is 12cm, ∠ a = 30 °, rotate the triangle plate ABC clockwise 90 ° around C to the position of triangle plate a'b'c ', and then translate it to the left along the CB direction, so that the point B' falls on the hypotenuse ab of the original triangle plate ABC, then the translation distance of triangle plate a'b'c 'is () A. 6cmB. 4cmC. （6-23）cmD. （43−6）cm
- 12. Take a pair of triangle ruler and splice it according to the way shown in Fig. 1, fix the triangle ruler ADC, and rotate the triangle ruler ABC clockwise around point a to get the triangle ruler Let's ask when α is how many degrees, can make ab ‖ DC? 2 rotate to the position of ③, then how many degrees is α?
- 13. In the known triangle ABC and triangle def, ab = 2 cm, BC = 3 cm, CA = 4 cm, de = 7.5 cm, EF = 10 cm, FD = 5 cm Like? Why?
- 14. As shown in the figure, in △ ABC, D is the point on AC, e is the point on CD extension line, and AC / BC = EF / DF, verification: ad = EB
- 15. It is known that the quadrilateral ABCD is a parallelogram, the bisector CF of ∠ BCD intersects AB at F, and the bisector DG of ∠ ADC intersects AB at G 1. Verification: AF = GB 2. Please add another condition on the basis of the known condition, so that Δ EGF is an isosceles right triangle
- 16. As shown in the figure, in the quadrilateral ABCD, ab ‖ CD, AE bisection ∠ bad intersects BC at point E, and ab = EB is proved. The quadrilateral ABCD is a parallelogram
- 17. It is known that in △ ABC, ad is the bisector of ∠ BAC outer angle ∠ EAC, and D is the intersection of bisector and BC extension Don't copy the answer
- 18. As shown in the figure, AC ', BD', Ca ', DB' are bisectors of the four inner angles of the planar quadrilateral ABCD Please find out all the parallelograms except for the parallelogram ABCD. No more letters will be added and one of them will be selected to prove that although we didn't learn 5.2 parallelograms from the figure,
- 19. As shown in the figure, ad is the angular bisector of angle cab, ed | AB, DF | Ca, EF intersects ad at point O. excuse me, (1) is do the angular bisector of angle EDF? If so, give a clear proof;
- 20. As shown in the figure, ad is the angular bisector of △ ABC, de ‖ AB, DF ‖ AC, EF intersects ad at point O. excuse me: is do the angular bisector of △ def? Please give reasons