Question 400735
<pre><font face = "batangche" color = "indigo" size = 4><b> 
{{{drawing(300,400,-1.5,1.5,-.5,3.5, 

line(-1,0,1,0), line(-1,0,0,3),line(0,3,1,0),line(-.7,.9,.7,.9),
line(-.75,7/15,-.9,31/60),line(.75,7/15,.9,31/60),

locate(1,0,C), locate(-1.1,0,A), locate(-.8,.95,D), locate (.75,.95,E),
locate(0,3.2,B)

 )}}}

Draw DF and EG &#8869; AC

{{{drawing(300,400,-1.5,1.5,-.5,3.5, 

line(-1,0,1,0), line(-1,0,0,3),line(0,3,1,0),line(-.7,.9,.7,.9),
line(-.75,7/15,-.9,31/60),line(.75,7/15,.9,31/60),
green(line(-.7,0,-.7,.9), line(.7,.9,.7,0)),locate(-.7,0,F),locate(.7,0,G),
locate(1,0,C), locate(-1.1,0,A), locate(-.8,.95,D), locate (.75,.95,E),
locate(0,3.2,B)
 )}}}

DF &#8869; AC            (drawn that way)

EG &#8869; AC            (drawn that way)

DF &#8741; EG             lines perpendicular to the same line are parallel

DE &#8741; FG             bases of a trapezoid are parallel 

FDEG is a parallelogram   (both pairs of opposite sides parallel)

DF &#8773; EG             Opposite sides of a parallelogram   

DA &#8773; EC             legs of isosceles trapezoid

&#5123;ADF and &#5123;CEG are right triangles  (DF and EG &#8741; AC)

&#5123;ADF &#8773; &#5123;CEG        hypotenuse-leg theorem

&#8736;A &#8773; &#8736;C         corresponding parts of congruent triangles ADF and CEG

&#5123;ABC is isosceles   base angles congruent.   

Edwin</pre>