Is it possible to prove that the triangles are congruent? if so state the postulate or theorem you would use.

Proving triangles are congruent: If 3 sides of one triangle are congruent to 3 sides of another triangle, then the two triangles are congruent. If 2 sides are congruent and the angle between the sides are congruent then the triangles are congruent. Try that.

Step-by-step explanation:

yes

step-by-step explanation:

yes

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