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Area   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Designer  Mr/mohamed ali  ,[object Object],[object Object],[object Object],[object Object],[object Object],geometry second prep Rotation rotation translation Elpharanna EX. L.S
the area of the square = the area of the colored figures
Rectangle with dimensions 4,9cm squarewith side length=6cm they have the same area
 
 
 
 
 
 
 
 
 
 
 
Area of  parallelogram with a common base and between two parallel straight line one of them if the common base are equal in area  theorem (1)
E F F E
Area of triangle is equal to half area of the paralllogram  which have the same base and between two parallel lines  M L K X Y
Two triangles have the same base and between two parallel  one of them the common base have the same area F F
Remark1 The median divide the triangle into two triangles equal in area
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
Y Y Y
(4,4) (2,1) (4,1) (-4,4) (-1,2) (-1,4) (-2,-1) (-4,-1) (-4,-4) (4,-4) (1,-2) (1,-4) A B C change the Y  sign then replace change the X,Y  without replacing change the X sing then replace 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 The image of the triangle ABC by a rotation  about the origin with an angle of measure 90 The image of the triangle ABC by a rotation  about the origin with an angle of measure 180 The image of the triangle ABC by a rotation  about the origin with an angle of measure 270
(4,4) (2,1) (4,1) (1,-2) A B C The image of the triangle ABC by a translation (-2,-3) 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
 

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Area

  • 1.
  • 2. the area of the square = the area of the colored figures
  • 3. Rectangle with dimensions 4,9cm squarewith side length=6cm they have the same area
  • 4.  
  • 5.  
  • 6.  
  • 7.  
  • 8.  
  • 9.  
  • 10.  
  • 11.  
  • 12.  
  • 13.  
  • 14.  
  • 15. Area of parallelogram with a common base and between two parallel straight line one of them if the common base are equal in area theorem (1)
  • 16. E F F E
  • 17. Area of triangle is equal to half area of the paralllogram which have the same base and between two parallel lines M L K X Y
  • 18. Two triangles have the same base and between two parallel one of them the common base have the same area F F
  • 19. Remark1 The median divide the triangle into two triangles equal in area
  • 20. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 21. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 22. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 23. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 24. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 25. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 26. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 27. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 28. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 29. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 30. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 31. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 32. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 33. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 34. The image of the point A with rotation of mesure 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 35. Y Y Y
  • 36. (4,4) (2,1) (4,1) (-4,4) (-1,2) (-1,4) (-2,-1) (-4,-1) (-4,-4) (4,-4) (1,-2) (1,-4) A B C change the Y sign then replace change the X,Y without replacing change the X sing then replace 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 The image of the triangle ABC by a rotation about the origin with an angle of measure 90 The image of the triangle ABC by a rotation about the origin with an angle of measure 180 The image of the triangle ABC by a rotation about the origin with an angle of measure 270
  • 37. (4,4) (2,1) (4,1) (1,-2) A B C The image of the triangle ABC by a translation (-2,-3) 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5
  • 38.