Question

In triangle abd, ci s the mid point of bd. If ab=10cm, ad=12cm and ac=9cm then bd=

Answer 1

Step-by-step explanation:

Given:  BO = OD

To prove: ar(∆ABC) = ar(∆ADC)

Proof: 

Since BO = OD, O is the mid point of BD.

We know that a median of a triangle divides it into two triangles of equal areas.

CO is a median of ∆BCD.

i.e., ar(∆COD) = ar (∆COB)            ...(i)

AO is a median of ∆ABD. 

i.e., ar(∆AOD) = ar(∆AOB)              ...(ii)

From (i) and (ii), we have:

ar(∆COD) + ar(∆AOD) = ar(∆COB) + ar(∆AOB)

∴ ar(∆ADC ) = ar(∆ABC)