Question

prove that a median divides a triangle into two triangles of equal area

Answer 1

Given

• A ΔABC
• AD is a median
• BD = DC

To prove

• ar (ΔABD) = ar(ΔADC)

Construction

• Draw AL ⊥ BC

Proof

• ar (ΔABD) = ½ × BD × AL (½ × Base × Height)
• ar (ΔADC = ½ × DC × AL  (BD = DC)

☯️ ∴ ar (ΔABD) = ar (ΔADC) = ½ ar (ΔABC)

Answer 2

Answer:

Consider a triangle ABC with CD as median.

Let AD=BD= b/2

As CD is median and height =h

So, area (△ADC)= 1/2 ×b/2 × h

area (△BDC)= 1/2 × b/2 × h

So, area of △ADC= area of △BDC

A median divides a triangle into two triangles of equal area, Hence proved.