Given triangle abc, what is a possible first step to prove the triangle inequality theorem?

draw a line segment perpendicular to bc through a.
draw a line segment through the midpoint of bc and point a.
draw a line parallel to bc through a.
draw a line segment through the midpoint of ac and point b.

b

step-by-step explanation:

the word superfluous means unnecessary

$15 each

step-by-step explanation:

$45/3 children= $15 each

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4