teral triangle ABC. AD is drawn nerpendicular to BC meeORIn an equilat

1.	teral triangle ABC. AD is drawn nerpendicular to BC meeORIn an equilateralProve that AD2= 3RDcuilar to BC meeting BCat D. ProB
Answer» In an equilateral triangle ABC ,AB = BC = ACAD⟂ BCAD is also the perpendicularbisector of the side BC.Hence,BD = DCAlso,BC = 2 BD According to Pythagoras theorem,InΔADB, AB² = AD² + BD² AD² = AB² - BD² AB = BC , AD² = BC² - BD² AD² = (2BD)² - BD² AD² = 4BD² - BD² AD² = 3BD²

teral triangle ABC. AD is drawn nerpendicular to BC meeORIn an equilateralProve that AD2= 3RDcuilar to BC meeting BCat D. ProB

Answer»

In an equilateral triangle ABC ,AB = BC = ACAD⟂ BCAD is also the perpendicularbisector of the side BC.Hence,BD = DCAlso,BC = 2 BD

According to Pythagoras theorem,InΔADB,

AB² = AD² + BD²

AD² = AB² - BD²

AB = BC ,

AD² = BC² - BD²

AD² = (2BD)² - BD²

AD² = 4BD² - BD²

AD² = 3BD²