if through the midpoint of base of triangle a straight line is drawn parallel to one of two remaining sides of a triangle prove that its intercept on internal and external bisectors of vertical angles is equal to its 3rd side
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Given
From the figure,
Where, AC has mid point E.
In ΔBEC,
It has mid point D and median ED.
\ar BDE = \ar CDE -----> ( 1 )
Where, "\ar" represents area of the triangle.
DE base is common for ΔADE and ΔBDE and DE lies between the same parallel DE and AB.
\ar ADE = \ar BDE -----> ( 2 )
From ( 1 ) and ( 2 ),
\ar BDE + \ar ADE = \ar CDE + \ar BDE
\ar ADE = \ar CDE -----> ( 3 )
Where, DE divides ΔADC into two parts of equal area.
Therefore, DE is median and mid point.
To learn more...
1. brainly.in/question/5698081
2. brainly.in/question/2636809
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