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Use counterexamples to test conjectures
Worksheet
Grade Level
Geometry
GEO.18 Use counterexamples to test conjectures
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Conjecture: In any triangle, the orthocenter and the circumcenter are the same point. Which option is a counterexample?
A
An equilateral triangle (all centers coincide)
B
A right triangle (orthocenter at the right-angle vertex; circumcenter at the midpoint of the hypotenuse)
C
A statement: the circumcenter is where perpendicular bisectors meet
D
A statement: the orthocenter is where altitudes meet
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