A controversial "converse theorem" (Reply to the previous one)
Asked by T S | 23rd Dec, 2013, 05:14: PM
First consider the theorem. This theorem is based on the assumption that
one of the parallels is the base of the triangle.
Fix this assumption that one of the parallels is the base of the triangle.
Now, consider the converse. In the diagram that you have provided, neither
of the two parallels is the base. Since it is violating the assumption,
the theorem cannot be applied to this situation.
The aim of the theorem is to show that if
Area = (1/2) * Base * Height
and Base value and Area value are equal,
the Height value is also equal.
In the theorem, the Height value is represented as the distance between 2
Due to the motive of the theorem, the Height value is thus,
the distance between the base and a line parallel to the base.
So, the representation of the triangles doesnot matter. It doesnot matter
if the two triangles are inverted because, the notion of parallellism comes form
the notion of the Height of the trianlges.
Answered by Vimala Ramamurthy | 24th Dec, 2013, 09:08: AM
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