In Fig., E is any point on median AD of a ∆ABC. Show that ar. (ABE)

1.	In Fig., E is any point on median AD of a ∆ABC. Show that ar. (ABE) = ar.(ACE).
Answer» Data: E is any point on Median AD of an ∆ABC. To Prove: ar.(∆ABE) = ar. (∆ACE) Proof: In ∆ABC, AD is the median. ∴ ∆ABD = ∆ACD ……….. (i) In ∆EBC, DE is the median. ∴ ∆EBC = ∆ECD …………. (ii) Subtracting (ii) from (i), ∆ABD – ∆EBD = ∆ACD – ∆ECD ∴ ar. (∆ABE) = ar. (∆ACE).

In Fig., E is any point on median AD of a ∆ABC. Show that ar. (ABE) = ar.(ACE).

Answer»

Data: E is any point on Median AD of an ∆ABC.

To Prove: ar.(∆ABE) = ar. (∆ACE)

Proof: In ∆ABC, AD is the median.

∴ ∆ABD = ∆ACD ……….. (i)

In ∆EBC, DE is the median.

∴ ∆EBC = ∆ECD …………. (ii)

Subtracting (ii) from (i),

∆ABD – ∆EBD = ∆ACD – ∆ECD

∴ ar. (∆ABE) = ar. (∆ACE).