# SOLUTION: Solve the proof...This is so confusing. Given (AB) &#773;&#8773;(AE) &#773; (BC) &#773;&#8773;(DE) &#773; Prove <1&#8773;<2 I cannot paste the figure so I will describe it. It

Algebra ->  Algebra  -> Triangles -> SOLUTION: Solve the proof...This is so confusing. Given (AB) &#773;&#8773;(AE) &#773; (BC) &#773;&#8773;(DE) &#773; Prove <1&#8773;<2 I cannot paste the figure so I will describe it. It       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Question 590393: Solve the proof...This is so confusing. Given (AB) ̅≅(AE) ̅ (BC) ̅≅(DE) ̅ Prove <1≅<2 I cannot paste the figure so I will describe it. It is a triangle with A on the top and B, C, D, E at the bottom. In the middle of the triangle is C and D is 1 above C and 2 above D. A 1 2 B C D EAnswer by solver91311(16897)   (Show Source): You can put this solution on YOUR website! Since segment AB and segment AE are congruent (given), the triangle ABE must be isoscles by definition of an isosceles triangle. From that it follows that angle ABC must be congruent to angle AED, again by definition of an isosceles triangle. Then because you are given that segment BC and segment DE are congruent, triangle ABC must be congruent to triangle AED by SAS. Now you aren't clear whether angle 1 is angle ACB or ACD. Assume it is ACB, then ACB is congruent to ADE by CPCT. Therefore angle 1 equals angle 2. QED. If angle 1 is ACD and angle 2 is ADC, then since angle ACB is supplementary to angle ACD, angle ADE is supplementary to angle ADC, and from the step above angle ACB is congruent to angle ADE, then angle ACD is congruent to angle ADC by transitive equality. Therefore angle 1 equals angle 2. QED. John My calculator said it, I believe it, that settles it