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  # Solution - Show that the Diagonals of a Parallelogram Divide It into Four Triangles of Equal Area. - CBSE Class 9 - Mathematics
  
  ConceptTriangles on the Same Base and Between the Same Parallels
  
  #### Question
  
  Show that the diagonals of a parallelogram divide it into four triangles of equal area.
  
  #### Solution
  
  We know that diagonals of parallelogram bisect each other.
  
  Therefore, O is the mid-point of AC and BD.
  
  BO is the median in ΔABC. Therefore, it will divide it into two triangles of equal areas.
  
  ∴ Area (ΔAOB) = Area (ΔBOC) ... (1)
  
  In ΔBCD, CO is the median.
  
  ∴ Area (ΔBOC) = Area (ΔCOD) ... (2)
  
  Similarly, Area (ΔCOD) = Area (ΔAOD) ... (3)
  
  From equations (1), (2), and (3), we obtain
  
  Area (ΔAOB) = Area (ΔBOC) = Area (ΔCOD) = Area (ΔAOD)
  
  Therefore, it is evident that the diagonals of a parallelogram divide it into four triangles of equal area.
  
  Is there an error in this question or solution?
  
  #### APPEARS IN
  
  NCERT Mathematics Textbook for Class 9
  Chapter 9: Areas of Parallelograms and Triangles
  Q: 3 | Page no. 162
  
  #### Reference Material
  
  Solution for question: Show that the Diagonals of a Parallelogram Divide It into Four Triangles of Equal Area. concept: Triangles on the Same Base and Between the Same Parallels. For the course CBSE
  S
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