Question

Prove that the pedal triangle of an equilateral triangle is also an equilateral triangle

Answer 1

Answer:

Step-by-step explanation:

When ΔABC is equilateral, then the medians are the perpendicular bisectors of each side.

Thus, we know that R, S, and T are the midpoints of each side.

This implies that$\frac{}{RS}//\frac{}{AC} ,\frac{}{ST}//\frac{}{AB},\frac{}{RT} //\frac{}{BC}$

and

$\frac{}{RS} =\frac{1}{2} \frac{}{AC},  \frac{}{ST} =\frac{1}{2}\frac{}{AB},  \frac{}{RT}=\frac{1}{2} \frac{}{BC}$

(by the midpoint theorem).

Hence  , $\frac{}{RS}=\frac{}{ST}= \frac{}{TR}$which shows us that the pedal triangle is equilateral!