Question 1191655
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Here is a diagram....<br>
{{{drawing(600,400,-8,8,-2,30
,line(-5,0,5,0),line(-5,0,2,28),line(0,20,5,0),line(2,0,2,28)
,locate(-5,0,B),locate(5,0,C),locate(-1,20,A),locate(2,0,F),locate(2.5,12,E),locate( 2.5,28,D)
,locate(-4,2,x),locate(4,2,x)
)}}}<br>
We are given AB = AC, so angles BCA and CBA are congruent. Let x be the measure each of those angles.  Then...<br>
(1) In triangle CFE, the measure of angle CEF is 90-x.
(2) in triangle BFD, the measure of angle BDF is 90-x.
(3) In triangle ADE, the measure of angle AED is 90-x, because it is a vertical angle with angle FEC.<br>
So we have congruent angles ADE and ADE in triangle ADE; therefore triangle ADE is isosceles.<br>