Question

ABC be a triangle on which D is a point on BC such that BD = CD. From D, the perpendiculars are drawn to the sides of the triangle. If the perpendicular are equal them to prove that AB = AC.

Answer 1

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In △ ABD and △ ADC

AD = AD (common)

BD = CD (given)

AB = AC (given)

Hence,

△ ABD ≅ △ ADC ( SSS )

So,

∠ADB = ∠ADC = x ( By CPCT )

∠ADB = ∠ADC = 180° ( Angles on a straight line )

x + x = 180°

2x = 180°

$x = \frac{180}{2}$

x = 90°

∠ADB = ∠ADC = 90°

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