As shown in the figure, in the trapezoid ABCD, BC ‖ ad, ab = BC = CD = 2, ad = 4. The known point a coordinates are (- 2,0). Try to find the other three vertex coordinates of the trapezoid ABCD
D (2.0) B (- 1, radical 3), C (1, radical 3)
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- 1. If a circle passes through four vertices of a trapezoid ABCD, then the trapezoid is isosceles ∵AD∥BC, ∴∠A+∠B=180°, ∵∠A+∠C=180°, ∴∠B=∠C, The trapezoid ABCD is isosceles trapezoid; Why ∵ a + C = 180?
- 2. 2. (2010 Qingdao, Shandong Province) fold a rectangular piece of paper (rectangular ABCD) as shown in the figure, so that vertex B and point d coincide, crease
- 3. As shown in the figure, the rectangle ABCD with the length of 2 and the width of 1 rotates 90 ° clockwise with the top of the lower right corner as the center, and the coordinate of point a is_______ . turn 2 in turn The rectangle ABCD with length of 2 and width of 1 is rotated 90 ° clockwise with the vertex in the lower right corner as the center, and the coordinate of point a is_______ . rotate 2009 times in turn, then the coordinate of vertex A is________ .
- 4. As shown in the figure, the vertices a and B of rectangle ABCD are on the number axis, CD = 6, and the number corresponding to point a is - 1, then the number corresponding to point B is______ .
- 5. As shown in the figure, the vertices a and B of rectangle ABCD are on the number axis, CD = 6, point E is the midpoint of AB, and the digit corresponding to point a is - 1, then the number corresponding to point E is
- 6. As shown in the figure, the vertices a and B of rectangle ABCD are on the number axis, CD = 6, and the number corresponding to point a is - 1, then the number corresponding to point B is______ .
- 7. (2010 Hebei) the vertices a and B of rectangle ABCD are on the number axis, CD = 6, the number corresponding to point a is - 1, then the number corresponding to point B is -. I think it is 5 or - 7
- 8. As shown in the figure above, the coordinates of the four vertices of the quadrilateral ABCD are a (- 2,0), B (1,7) and C (5,5) As shown in the figure above, the coordinates of the four vertices of the quadrilateral ABCD are a (- 2,0), B (1,7), C (5,5) D (7,0) tries to find the area of this quadrilateral; As shown in the figure above, the coordinates of the four vertices of the quadrilateral ABCD are a (- 2,0), B (1,7), C (5,5) D (7,0) try to find the area of this quadrilateral;
- 9. There are two points a (1,7) and B (3,4) in the plane rectangular coordinate system. How to find a point C and D on the x-axis and y-axis to minimize the perimeter of the quadrilateral ABCD?
- 10. Given that point a (1,2) and point B (5,6) are of length 1, the segment CD moves on the x-axis. When the perimeter of quadrilateral ABCD is the smallest, the coordinate of point D is ()
- 11. Given that the coordinates of the three vertices of ladder ABCD are a (- 2,3), B (- 2,1), C (6,5), the equation of the straight line of the median line of the ladder is obtained
- 12. Let the vertex coordinates of ladder ABCD be a (- 1,2), B (3,4), D (2,1) and ab parallel to DC, the length of AB = 3 times the length of CD, then the coordinate of C is
- 13. In rectangular trapezoid ABCD. Ad = 7 & nbsp; & nbsp; ab = 2 & nbsp; & nbsp; DC = 3 & nbsp; & nbsp; P is a point on ad. the triangle with the vertex of P, a and B is similar to the triangle with the vertex of P, D and C. how many such points P have? Why?
- 14. Vertex a (- 2,2), B (- 1,4), C (4,5 +) of ladder ABCD, and AB / / DC, ab = 1 / 2dc, find the coordinates of vertex D Correction, C (4,5)
- 15. If the vertex a (- 1,2) B (3,4) d (2,1) of ladder ABCD and ab ‖ DC, ab = 2CD, then the coordinate of point C is?
- 16. Let the vertex coordinates of ladder ABCD be a (- 1,2), B (3,4), D (2,1), and ab is parallel to DC, ab = 2 DC, then the coordinates of point C are obtained AB = 2 DC with arrow (plane vector)
- 17. Given the three vertices a (1,2), B (3,4) and C (2,6) of ladder ABCD, find the point direction equation of the straight line where the median line of the ladder is located?
- 18. The ratio of the top to the bottom of a trapezoid is 3 / 5. The top is 1 meter shorter than the bottom, and the bottom is 25% higher. What is the area of this trapezoid?
- 19. The figure on the right is a trapezoid. If the bottom is extended by one fourth, and the upper bottom and height remain unchanged, the new trapezoid is 76 square centimeters larger than the original trapezoid. Calculate the area of the original trapezoid
- 20. The area of the new trapezoid is increased by 76 square centimeter if the bottom is lengthened by 1 / 4 and the height and upper bottom remain unchanged