# SOLUTION: Given: ADEC is an Isosceles Trapezoid Prove: ABC is an Isosceles Triangle

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 Question 400735: Given: ADEC is an Isosceles Trapezoid Prove: ABC is an Isosceles TriangleAnswer by Edwin McCravy(8893)   (Show Source): You can put this solution on YOUR website!``` Draw DF and EG ⊥ AC DF ⊥ AC (drawn that way) EG ⊥ AC (drawn that way) DF ∥ EG lines perpendicular to the same line are parallel DE ∥ FG bases of a trapezoid are parallel FDEG is a parallelogram (both pairs of opposite sides parallel) DF ≅ EG Opposite sides of a parallelogram DA ≅ EC legs of isosceles trapezoid ᐃADF and ᐃCEG are right triangles (DF and EG ∥ AC) ᐃADF ≅ ᐃCEG hypotenuse-leg theorem ∠A ≅ ∠C corresponding parts of congruent triangles ADF and CEG ᐃABC is isosceles base angles congruent. Edwin```