In triangle ABC shown below, side AB is 6 and side AC is 4: Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Segment AD is 3, and segment AE is 4.
Segment AD is 3, and segment AE is 2.
Segment AD is 12, and segment AE is 8.
Segment AD is 12, and segment AE is 4.

idk

step-by-step explanation:

answer: h

step-by-step explanation:

x = 23.78

step-by-step explanation:

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