ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.

Question

Philoid · Accepted Answer

Given: ΔABC is an isosceles triangle and AB = AC, BD and CE are two medians.

In ΔABD and ΔACE,

AB = AC (given)

We can write it as:

2 AE = 2 AD (as D and E are mid points)

So, AE = AD

∠A = ∠A (common)

Hence, ΔABD ≅ ΔACE (using SAS)

⇒ BD = CE (by CPCT)

Hence proved.