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

Answer:

ANSWER

In △s ABD and ADC,

AD = AD (Common)

BD = CD (Given)

AB = AC (Given)

Hence, △ABD≅△ADC (SSS rule)

Thus, ∠ADB=∠ADC=x (By cpct)

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

x+x=180

x=90

∠ADB=∠ADC=90

∘

or, AD is perpendicular to BC

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