Question

State true or false:

In the given figure;
$AD$ is median of $△ABC$ and $E$ is any point on median $AD$. Prove that Area $(△ABE)$ = Area $(△ACE)$

• A. True
• B. False

Answer 1

The correct option is A True

Given, AD is median of triangle ABC and E is the any point on median AD.
Since, AD is median of $△ABC$ and median divides the triangle into two triangles of equal area.
$\therefore$ Area of $△ABD$$=$Area of $△ADC$ ..(1)
Again, In $△BEC$, D is mid point of BC. So,DE is median of $△BEC$ and median divides the triangle into two triangles of equal area.
$\therefore$ Area of $△BED$$=$Area of $△DEC$ ..(2)
From (1),
Area of $△ABD$$=$Area of $△ADC$
or, Area of $△ABE$$+$Area of $△BED$$=$ Area of $△ACE$$+$Area of $△DCE$
Eliminating, Area of $△BED$ and Area of $△DCE$ from both sides as they are equal. (From 2)
$\therefore$ Area of $△ABE$$=$Area of $△ACE$