Question 1059693

1.{{{PQ^2=PR^2+QR^2}}}
2.{{{SQ^2+RS^2=QR^2}}}
3.{{{PR^2=RS^2+PS^2}}}
{{{PQ=QS+SP=6+2=8}}}
Substituting into 1, 2, and 3,
{{{8^2=PR^2+QR^2}}}
{{{PR^2+QR^2=64}}}
.
.
{{{6^2+RS^2=QR^2}}}
{{{36+RS^2=QR^2}}}
.
.
{{{PR^2=RS^2+2^2}}}
{{{PR^2=RS^2+4}}}
.
.
{{{(RS^2+4)+(36+RS^2)=64}}}
{{{2RS^2+40=64}}}
{{{2RS^2=24}}}
{{{RS^2=12}}}
So then,
{{{RS^2=12}}}
{{{PR^2=12+4}}}
{{{PR^2=16}}}
{{{PR=4}}}
True