Question

In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]

Answer 1

Concept : 0.5 Mark
Application : 0.5 Mark
Calculation : 1 Mark

AD is the median of $△$ABC. Therefore, it will divide $△$ABC into two triangles of equal areas.

Therefore, Area ($△$ABD) = Area ($△$ACD) ... (1)

ED is the median of $△$EBC.

Therefore, Area ($△$EBD) = Area ($△$ECD) ... (2)

On subtracting equation (2) from equation (1), we obtain

Area ($△$ABD) − Area ($△$EBD) = Area ($△$ACD) − Area ($△$ECD)

Area ($△$ABE) = Area ($△$ACE)