Ceva’s Theorem

1. Ceva’s Theorem By Blake, David, Farah, Mark and Taylor

2. Aim: How can Ceva’s Theorem help to prove similar triangles? Do Now: List three ways to prove a similar triangle. AA – Angle Angle SSS- When three pairs of corresponding sides are in the same ratio SAS- Two sides and the included angle of one triangle are in the same ratio as the corresponding two sides and included angle in another triangle

3. A Brief history… • Giovanni Ceva (1648-1734) was a Italian mathematician who studied geometry • Ceva rediscovered and republished Menelaus’s Theorem • Ceva wrote De Re Nummeraria, which was one of the first books of its kind in mathematical economics • He published a theorem on synthetic geometry in a triangle, Ceva’s theorem, in De lineisrectis. • Ceva’s theorem states…

4. Aim: How can Ceva’s Theorem help to prove similar triangles? If three line segments are drawn from the vertices of a triangle to their opposite sides, then the three line segments are concurrent if, and only if, the product of the ratios of the newly created line segments on each side of the triangle is equal to one.

5. Let’s prove the theorem!