Question 1079704
{{{drawing(6200/9,400,-1,28/3,-1,5,

triangle(0,0,3,4,3,0),triangle(3,4,3,0,25/3,0),
locate(0,0,S), locate(3,0,U), locate(25/3,0,T),locate(3,4.4,R))}}}
<pre>
&#8737;T &#8773; &#8737;T          reflexive property
&#8737;SRT &#8773; &#8737;RUT      both are right angles
&#916;STR &#8765; &#916;RTU      two angles congruent in each

{{{TU/(RT)}}}{{{""=""}}}{{{RT/ST}}}   CPST

{{{TU*ST}}}{{{""=""}}}{{{RT^2}}}    Cross-multiplying

---

&#8737;S &#8773; &#8737;S          reflexive property
&#8737;SRT &#8773; &#8737;SUR      both are right angles
&#916;STR &#8765; &#916;SRU      two angles congruent in each

{{{AE/(RS)}}}{{{""=""}}}{{{RS/ST}}}   CPST

{{{AE*ST}}}{{{""=""}}}{{{RS^2}}}      Cross-multiplying

{{{TU*ST+SU*ST}}}{{{""=""}}}{{{RT^2+RS^2}}}  Equals added to equals

Factor out ST on the left side:

{{{ST(TU+SU)}}}{{{""=""}}}{{{RT^2+RS^2}}}

TU+SU = ST                     Whole = sum of parts

{{{ST(ST)}}}{{{""=""}}}{{{RT^2+RS^2}}}  Replacing equal by equal

{{{ST^2}}}{{{""=""}}}{{{RT^2+RS^2}}}   

Same as what you had to prove.

Edwin</pre>