Question

prove that a median divides a triangle in to two triangles of equal area .​

Answer 1

this is required answer for your question

Answer 2

Question :

Prove that a median divides a triangle into two triangles of equal area .

Solution :

Given :

∆ QRS with QT as median.

To prove :

$Area (∆ QRT) = Area (∆ QTS ) = \frac{1}{2} Area ( ∆</strong><strong> </strong><strong>QRS</strong><strong>)$

Construction needed : Draw QU _|_ RS

Let's Proof :

Since,

$Area \: of \: a \: ∆ = \frac{1}{2} base \: \times height \:$

$\: Area \: (∆ QRT) = \: \frac{1}{2} \times RT × QU$

and,

$Area \: (∆ QTS ) = \frac{1}{2} \times \:TS × QU$

$= \: \frac{1}{2} \times RT × QU$

$Therefore \: Area \: of \: ∆ QRT \: = \: Area \: of \: ∆ \: QTS = \frac{1}{2} \: Area \: of (∆ QRS) </p><p> </p><p>$

Hence Proved.

Note : Refer the attachment for better understanding.