Question

Abc is an isosceles triangle with ab=ac and bd and ce are its median. Show that bd=ce

Answer 1

ok....

Abc is an isosceles triangle with ab=ac and bd and ce are its median. Show that bd=ce

Given

ab=ac

bd and ce are median

prove... bd=ce

please..... attach figure.....

Answer 2

*Refer to the attachment for figure*

$\huge\underline\mathfrak\orange{Explanation-}$

Given :

• ABC is an isosceles triangle, in which AB = AC.
• BD and CE are its median.

To prove :

• BD = CE

Solution :

In ∆ABC, D and E are the mid points of sides AC and AB respectively as BD and CE are medians.

$\therefore$ AE = BE and AD = CD......(1)

Also, it is given that AB = AC

$\implies$ AE + BE = AD + CD

From (i),

$\implies$ BE + BE = CD + CD

$\implies$ 2BE = 2CD

$\implies$ $\cancel{2}$BE = $\cancel{2}$CD

$\implies$ BE = CD ........(ii)

__________________

Now,

In ∆BEC and ∆CDB,

• BE = CD ( proved above )
• Angle B = Angle C ( Angles opposite to equal sides are equal as AB = AC )
• BC = CB ( common side )

$\therefore$ ∆BEC is congruent to ∆CDB

$\implies$ CE = BD ( corresponding parts of congruent ∆s are equal )

Hence proved!