## Elementary Geometry for College Students (6th Edition)

$AF = s-a$
We can write an equation for each side of $\triangle ABC$: $BD+CD = a$ $AE+CE = b$ $AF+BF = c$ Then: $BD+CD + AE+CE + AF+BF = a+b+c$ $BD+CD + AF+CD + AF+BD = a+b+c$ $2BD+2CD + 2AF = a+b+c$ $BD+CD + AF = \frac{1}{2}(a+b+c)$ $BD+CD + AF = s$ $a + AF = s$ $AF = s-a$