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abcd is a parallelogram ac is diagnol ,so it divides into 2 triangles?so prove that areas of 2 triangles are equal??and  diagnols of parallelogram are equal or not??

 Sep 2, 2015
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Look at the following, matsunnymat  :

 

 

 

 

To prove that AC divides the parallelogram into two equal parts.......note that, by the defintion of  parallelogram,  angle (ABC)  = angle (CDA) ......   and AD = BC and AB = DC

 

Therefore, by SAS, triangle CDA = triangle ABC.....and if two triangles are equal [congruent, in this case ], their areas are also equal

 

 

In general......the diagonals of a parallelogram are not equal [except for squares and rectangles ]

 

For example.....the diagonal drawn from D to B above has a length of about 8.25....but the diagonal drawn from A  to C   has a length of only about 2.82

 

 

 

cool cool cool

 Sep 3, 2015

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