Question 1141290
Given: Line AB is parallel to line CD; line EC is congruent to line ED
Prove: Angle 1 is congruent to angle 2. 

1. {{{AB}}} ||{{{ CD}}}............given
2.{{{EC}}}  congruent {{{ ED}}}............given
3. <{{{ECD}}} congruent <{{{CDE}}}.........................the Isosceles Triangle Theorem
 4.<{{{ECD}}} congruent <{{{2}}}.................... Alternate Interior Angles are equal
5.<{{{CDE}}} congruent <{{{1}}}....................Alternate Interior Angles are equal

6. <{{{1}}} congruent <{{{2}}}..............transitive property


{{{drawing ( 600,600, -5, 10, -5, 10, 
circle(1,0,.12),locate(1,-0.5,C),
circle(9,0,.12),locate(9,-0.5,D),
circle(5,6,.12),locate(5,6,E),
line(1,0,5,6),line(9,0,5,6),line(1,6,9,6),locate(9,6,B),locate(1,6,A),locate(3,5,1),locate(7,5,2), locate(1.5,0.5,ECD),locate(8,0.5,CDE),
graph( 600,600, -5, 10, -5, 10, 0)) }}}