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Q.

Tell whether the following statement is true or false:


In a triangle ABC, if E is the midpoint of median AD, then area of triangle BED =  1 4   of area of triangle ABC.


In a triangle ABC, E is the midpoint of median AD. Show that from  Mathematics Areas of Parallelograms and Triangles Class 9 Punjab Board

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a

True

b

False 

answer is A.

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Detailed Solution

Given a triangle ABC in which E is the midpoint of median AD.
In a triangle ABC, E is the midpoint of median AD. Show that from  Mathematics Areas of Parallelograms and Triangles Class 9 Punjab BoardAD is median and the median divides the triangle into 2 parts having equal area.
Area of triangle ABD = 1 2   area of triangle ABC
Similarly, BE is median,
Area of triangle BED = 1 2   area of triangle ABD
Now, combining both equations.
Area of triangle BED = 1 4   area of triangle ABC
Given statement is true.
Hence, option 1 is correct.
 
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