Counterexample angle bisector?

Melanie said:  
Every angle bisector in a triangle bisects the opposite side perpendicularly.

A 'counterexample' would show an angle bisector in a triangle that DOESN'T
bisect the opposite side perpendicularly. 

See my attached drawing of a counterexample.

Both of the triangles that Melanie examined have equal sides on both sides 
of the angle bisector.  That's the only way that the angle bisector can bisect
the opposite side perpendicularly.  Melanie didn't examine enough different 
triangles. 

Part A: 4a-3

Part B: (3a-5b) × (3a+5b)

Step-by-step explanation:

16a² - 24a + 9

(4a)² - 2(4a)(3) + 3²

(4a - 3)² = side²

side = 4a - 3

9a² - 25b²

(3a)² - (5b)²

(3a - 5b)(3a + 5b)