Question

how to prove Ceva's theorem?​

Answer 1

Step-by-step explanation:

We will begin with a verification of Ceva's Theorem.

Given triangle ABC with cevians BG, AF and CE concurrent at point D, we wish to demonstrate that:

We begin by constructing altitudes h1 and h2. The area of triangle ABG [in the future, we will use the notation (ABG) to designate the area of triangle ABG] equals 0.5(AG)(h1) and (BGC) = 0.5(GC)h1. Also, (ADG) = 0.5(AG)(h2) and (DGC) = 0.5(GC)(h2). Thus,

and

Then,

Similar reasoning yields the equations

and

.

Thus,

By cancelation,