Median of a triangle divides it into two triangles with equal area

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Median of a triangle divides it into two triangles with equal area Let ∆ ABC have median AD Median AD divides ∆ ABC into two triangles of equal area ∴ Area ∆ ABD = Area ∆ ACD Let’s look the proof Theorem - Proof Given: ∆ABC with AD as the median To prove: ar (∆ABD) = ar (∆ACD) Proof: Since AD is the median D is mid-point of side BC ∴ BD = CD = 𝟏/𝟐 BC To find area , we use formula Area of triangle = 𝟏/𝟐 × Base × Altitude To find Height, we draw perpendicular from point A to BC Let AN ⊥ BC Area ∆ ABD BD is the base & AN is the altitude Thus, Area ∆ ABD = 1/2 × Base × Altitude Area ∆ ABD = 𝟏/𝟐 × BD × AN Area ∆ ACD CD is the base & AN is the altitude Thus, Area ∆ ACD = 1/2 × Base × Altitude Area ∆ ACD = 1/2 × CD × AN Since CD = BD Area ∆ ACD = 𝟏/𝟐 × BD × AN From (1) & (2) Area ∆ ACD = Area ∆ ACD Hence proved