Geometry Problem 1559: Proving BC Bisects Segment DE. This geometry problem challenges students at high school and college levels

In triangle ABC, construct exterior triangles ABD and BCE in a way that angles ACB, CBE, and ABD are congruent, and angles DAB and BCE are also congruent. Your task is to prove that BC bisects segment DE.

Illustration of Geometry problem 1559 triangle ABC with exterior triangles ABD and BCE.

In the triangle's hold,
Exterior realms unfold,
Congruence, the gold.
BC bisects with proof's embrace,
Geometry's elegant grace.

Academic Levels: Suitable for High School and College Mathematics Education

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