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Geometric Proofs


Problems

Prove the following statements indirectly.

Problem :


Given:
Triangle ABC is an isosceles triangle with base AC.
Segment BE is a median.
Prove:
Segment BE is an angle bisector.


Problem :


Given: Circle F is inscribed in triangle ABC.
Prove: Angle DCF is congruent to angle ECF.


Problem : Use indirect reasoning to explain why a triangle cannot have more than one obtuse angle.