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Geometric Proofs


Indirect Proof

How to Cite This SparkNote

Prove the following statements indirectly.

Problem :

Triangle ABC is an isosceles triangle with base AC.
Segment BE is a median.
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.

First, assume that a triangle does have more than one obtuse angle. The measure of an obtuse angle is greater than 90 degrees. Hence, the sum of the measures of two obtuse angles is greater than 180 degrees, and the sum of the measures of three obtuse angles is greater that 270 degrees. The sum of the angles of a triangle, however, equals 180 degrees. Therefore, only one angle in a triangle can be obtuse.