In the above bridge, line segment bd is the perpendicular bisector of line segment ac. for the bridge to be safe, triangle abd is congruent to triangle cbd. considering strictly the information that was given, what sequence of reasons can you use to prove that triangle abd is congruent to triangle cbd?

SAS postulate will be use to prove  Δ ABD ≅ ΔCBD

Step-by-step explanation:

Here, In ΔABC line segment BD is the perpendicular bisector of line segment AC,

Therefore, BD ⊥ AC and, AD=DC

Thus, In triangles ABD and CBD,

AD≅DC     ( given)

∠ADB≅∠CDB ( Right angles)

BD≅BD            ( Reflexive)

Therefore, By SAS postulate of congruence,

Δ ABD ≅ ΔCBD.

C

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