# SOLUTION: TriangleABC and Triangle DAC are two isosceles triangle with angle BAC=20 and angle ADC=100.Show that AB=BC+CD.

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 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Question 331516: TriangleABC and Triangle DAC are two isosceles triangle with angle BAC=20 and angle ADC=100.Show that AB=BC+CD.Answer by Edwin McCravy(8908)   (Show Source): You can put this solution on YOUR website! ``` Locate point E so that triangle EAB is congruent to triangle DAC Draw ED Extend BC to F so that CF = CD. Draw DF I won't go through every step. I'll just tell you enough so you can write it out like your teacher wants you to. Using the fact that isosceles triangles have equal base angles, that interior angles of a triangle have sum 180°, that supplementary angles have sum 180°, and that vertical angles are equal, you can now write the number of degrees in every angle in the figure. That would be a good idea. Therefore it is easy to show that angle EAD = 100° = angle ADC = angle AEB. Then by SAS, triangles ADC, AEB and AED are all congruent. So AB = ED. It is easy to show that angle DCF = 60° and that triangle CFD is equilateral. You then show that BFDE is a parallelogram because angle F = 60° = angle BED , angle EBF = 120° = angle EDF. Then AB = ED = BF = BC + CF and since CF = CD, then AB = BC + CD. If you have any questions as to why anything is true, you can ask me in your thank-you note and I'll answer. Edwin```