Question

D and e are the points on sides ab and ac respectively of triangle abc such that area of triangle dbc is equal to area of triangle ebc prove that de parallel to bc

Answer 1

Given: D and E are points on sides AB and AC respectively of ΔABC and area (ΔDBC) = area (ΔEBC)

Construction: Construct two perpendiculars from points D and E on BC.



 

We know that Area of Any triangle is  

 

Since, Area of ΔDBC and ΔEBC are same and the base BC is common for both the triangles

So, the height of ΔDBC  is also equal to the height of ΔBEC 

⇒ h1 = h2

We know if the distance between two lines is equal, then the lines are parallel.

Hence  BC || DE.