Question

ABC an equilateral triangle, AD and BE are
perendiculars to BC and AC respectively. Prove that
1. AD = BE
2. BD = CE​

Answer 1

Answer:

In ΔABC 

AB=BC=CA 

We know that 

AD is perpendicular to BC and BE is perpendicular to AC

In ΔADC and ΔBEC 

∠ADC=∠BEC=90∘ 

∠ACD=∠BCE is common 

AC=BC are the sides of an equilateral triangle 

ΔADC≅ΔBEC (AAS Axiom) 

BD=CE (c.p.c.t)

Therefore , it is proved.

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