in an equilateral triangle ABC AD is perpendicular to BC find ratio AD square to BC square
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Hi !
In an equilateral triangle ABC ,
AB = BC = AC
AD ⟂ BC
AD is also the perpendicular bisector of the side BC.
Hence, BD = DC
Also,
BC = 2 BD
According to Pythagoras theorem,
In ΔADB,
AB² = AD² + BD²
AD² = AB² - BD²
AB = BC ,
AD² = BC² - BD²
AD² = (2BD)² - BD²
AD² = 4BD² - BD²
AD² = 3BD²
Proved.
In an equilateral triangle ABC ,
AB = BC = AC
AD ⟂ BC
AD is also the perpendicular bisector of the side BC.
Hence, BD = DC
Also,
BC = 2 BD
According to Pythagoras theorem,
In ΔADB,
AB² = AD² + BD²
AD² = AB² - BD²
AB = BC ,
AD² = BC² - BD²
AD² = (2BD)² - BD²
AD² = 4BD² - BD²
AD² = 3BD²
Proved.
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