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Indirect Proofs
GEOMETRY
DATE __________ Per.___________
Indirect Reasoning
1.
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NAME_________________________
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a) Use this diagram to state the Converse
of the Corresponding Angles Postulate:
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b) Use this diagram to assume the
opposite of what is to be proved.
c) Use indirect reasoning to prove the Converse of the Corresponding Angles Postulate as a
threorem. Establish that it contradicts the Triangle Exterior Angle Thoerem.
2.
Prove the Converse of the Alternate Interior Angle Theorem by indirect reasoning.
3. A right ∆ is defined to have only one right angle, and an obtuse ∆ only has one obtuse angle.
a) Indirectly prove a triangle can
have at most 1 right angle.
Assume ...
b) Write an indirect proof that
a triangle can’t have more than
1 obtuse angle.
4. Prove by contradiction that:
a) A quadrilateral can’t have four acute angles.
c) Prove a triangle must have
at least 2 acute angles.
b) A quadrilateral can’t have 4 obtuse angles.