Ceva's theorem: Difference between revisions

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'''Ceva's Theorem''' (pronounced "Cheva") is a very popular theorem in elementary [[geometry]].

Given a triangle ''ABC'', and points ''D'', ''E'', and ''F'' that lie on lines ''ABBC'', ''BCCA'', and ''CAAB'' respectively, the theorem states that

lines ''AD'', ''BE'' and ''CF'' are [[concurrent]] [[if and only if]]

:<math>\frac{AF}{FB} \cdot \frac{BD}{DC} \cdot \frac{CE}{EA} = 1.</math>

It was first proved by [[Giovanni Ceva]].

[[image:cevastheorem.jpg]]

==Proof==