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In the quadrilateral ABCD, it is known that angle A and angle c complement each other, and angle B is 15 degrees larger than angle D, then angle B =? Angle d =?
∠B=97.5°,∠D=82.5°
∵ in quadrilateral ABCD
Sum of internal angles = 360 degree
∴∠A+∠B+∠C+∠D=360°
∵∠A+∠C=180°
∴∠B+∠D=180°
∵∠B=∠D+15°
∴∠D+15°+∠D=180°
∠D=82.5°
∠B=82.5°+15°=97.5°
In plane rectangular coordinate system a (3,4) B (2, - 8) C (- 1, - 2) there is a process to find D point coordinate system a B C D to form a parallelogram
If AC is connected, the o coordinate of the midpoint of AC is: (1,1)
Let D (x, y), then: (2 + x) / 2 = 1 (- 8 + y) / 2 = 1
The solution is x = 0, y = 10
∴D(0,10)
In the plane rectangular coordinate system, if point a (3,4) and point B (4,0), please find another point C, which is O, a, B and C to form a parallelogram
Please write the coordinates of point C directly
C (- 1,4) or (7,4) or (1, - 4)
As shown in the figure: in the plane rectangular coordinate system, there are three coordinates of a (0,1), B (- 1,0), C (1,0). (1) if point D and a, B, C form a parallelogram, please write out the coordinates of all qualified points D; (2) select a qualified point D in (1), and find the analytical formula of straight line BD
(1) The coordinates of points D are D1 (2,1), D2 (- 2,1), D3 (0, - 1). (2) when D1 (2,1) is selected, let the analytic formula of line BD1 be y = KX + B, from the meaning of the question, we get - K + B = 02k + B = 1, and the solution is k = 13b = 13
RELATED INFORMATIONS
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- 2. There are several parallelograms whose vertices are three points a, B and C which are not on a straight line A. 1 B.2 C.3 D.4
- 3. Take a (0,0), B (4,0) C (2,3) as the vertex to draw a parallelogram and the coordinates of the fourth vertex D of the ball
- 4. Take three points a, B and C which are not on the same line as the three vertices to make parallelograms with different shapes. A total of () A. 1 B. 2 C. 3 d. 4
- 5. How many parallelograms can be made by taking three points not on the same line as three vertices?
- 6. In the plane rectangular coordinate system, a (- 2,0), B (0,1), C (0,4), take a, BC three points as the vertex to draw a parallelogram, then the fourth vertex
- 7. The coordinates of vertex a, B, D of parallelogram ABCD are a (0,0), B (2,2), D (4, - 3), respectively. Find the coordinates of point C and the area of parallelogram ABCD
- 8. In the parallelogram ABCD, ∠ a = ∠ C, ∠ B = ∠ D, is the quadrilateral ABC a parallelogram Why?
- 9. As shown in the figure, the quadrilateral ABCD is a parallelogram, ∠ ADC = 125 ° and ∠ CAD = 21 ° to calculate the degree of ∠ ABC and ∠ cab
- 10. It is known that: as shown in the figure, in the rectangular coordinate system xoy, one side of RT △ OCD OC is on the X axis. ∠ C = 90 °, point D is in the first quadrant, OC = 3, DC = 4, and the image of the inverse scale function passes through the midpoint a of OD. (1) find the analytical formula of the inverse scale function; (2) if the image of the inverse scale function intersects with the other side of RT △ OCD DC at point B, find the analytical formula of the straight line of a and B
- 11. If in the quadrilateral ABCD, the degree of a + C is equal to () A. 108°B. 180°C. 144°D. 216°
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- 13. Given a (0,3), B (- 1,0), C (3,0), the coordinates of point D are determined to make the quadrilateral ABCD an isosceles trapezoid
- 14. Given the vertices a (0, - 9), B (2,6), C (4,5) of the parallelogram ABCD, we can find the coordinates of the fourth fixed point D
- 15. In the plane rectangular coordinate system, a (1,3), B (2,1), OA ‖ BC, OC ‖ AB, try to use the knowledge of translation to find the coordinate of point C
- 16. As shown in the figure, the parabola y = 1 / 2x + MX + n (n ≠ 0) intersects the straight line y = x with two points AB, intersects the Y axis with points c, OA = ob, BC parallel to the X axis (1) The analytic formula of parabola (2) Let D and E be the two moving points on the line AB which are different from a and B (point E is above point d) de = root 2. Let D and E be parallel lines of Y axis, intersecting parabola and points F and g respectively. Let the abscissa of d be x and the area of quadrilateral degf be y. find the analytic expression of y about X, write out the value range of independent variable x, and find the maximum value of y when x is the value
- 17. As shown in Figure 1, in the quadrilateral ABCD, AB is perpendicular to ad, CD is perpendicular to ad, and BC is rotated 90 ° counterclockwise around point B to get the line segment be, connecting AE and Ce (1) As shown in Figure 1, in the quadrilateral ABCD, AB is perpendicular to AD and CD is perpendicular to AD. rotate BC 90 ° counterclockwise around point B to get the line segment be and connect AE and Ce (1). If AB = 2cm and CD = 3cm, calculate the area of triangle Abe
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- 19. As shown in the figure, in the plane rectangular coordinate system, the endpoint coordinates of line AB are a (- 2,4), B (4,2), and the line y = k X-2 has an intersection with line AB, then the value range of K is
- 20. As shown in the figure, line AB = a, O is the point on line AB, C and D are the midpoint of line OA and ob respectively 1. Find the length of CD; 2. If point O is on the extension line of AB, please draw a graph and explain