Question

Show that $△ABC$, where $A(-2,0),B(2,0),C(0,2)$ and $△PQR$ where $P(-4,0),Q(4,0),R(0,4)$ are similar triangles.

Answer 1

Given $A(-2,0);B(2,0);C(0,2)$ & $P(-4,0);Q(4,0);R(0,4)$

$AB=\sqrt{4^2+0}=4PQ=\sqrt{{(-8)}^2+0}=8$

$BC=\sqrt{4+4}=2\sqrt{2}QR=\sqrt{4^2+4^2}=4\sqrt{2}$

$AC=\sqrt{2^2+2^2}=2\sqrt{2}PR=\sqrt{{(-4)}^2+{(-4)}^2}=4\sqrt{2}$

$\Rightarrow \frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}=\frac{1}{2}$

$\therefore$ $\Delta ABC\sim \Delta PQR$ (SSS cong)