Question

In an equilateral $\Delta ABC,AD\perp BC$. prove that $A{D}^2=3B{D}^2$

Answer 1

We have, ΔABC is an equilateral Δ and AD ⊥ BC
In ΔADB and ΔADC
ADB = ADC { Each 90}
AB = AC {Given}
AD = AD {Common}
Then, ΔADB ΔADC [ By RHS condition]

BD = CD = $\frac{BC}{2}$ --- (i) Corresponding parts of similar triangles
In, ΔABD, by Pythagoras theorem

Hence proved