Question

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively . show that these altitudes are equal​

Answer 1

$answer$

ABC is an isosceles triangle in which altitudes BD and CE are drawn to equal sides AC and AB respectively .

Given ABC is an isosceles triangle

Then AB=AC

∴∠ABC=∠ACB

Or ∴∠EBC=∠DCB

In ΔEBC, ΔDCB.....................(1)

∠BEC=∠CDB=90°

BC=CB

∠EBC=∠DCB

ΔBEC≅ΔCFB.......(SAA test)

∴BD=EC

Then these altitudes are equal.