Let \( \Large P \left(1,\ 1\right),\ Q \left(-1,\ -1\right)\ and\ R \left(-\sqrt{3},\ \sqrt{3}\right) \)

\( \Large \triangle PQR \)

Therefore, \( \Large PQ=\sqrt{ \left(1+1\right)^{2}+ \left(1+1\right)^{2} }=\sqrt{8}=2\sqrt{2} \)

\( \Large QR=\sqrt{ \left(-\sqrt{3}+1\right)^{2}+ \left(\sqrt{3}+1\right)^{2} }=\sqrt{8}=2\sqrt{2} \)

Similarly, \( \Large PR=\sqrt{ \left(-\sqrt{3}-1\right)^{2}+ \left(\sqrt{3}-1\right)^{2} }=\sqrt{8}=2\sqrt{2} \)

=> \( \Large PQ - QR = PR \)

Which shows, triangle PQR is an equilateral