In the diagram, segments bg , cf , and de are parallel. the length of segment bd is 6.32 feet, and the length of segment de is 6 feet. find the lengths of segments bg and cf . bg= feet cf= feet

The complete question in the attached figure

we have that

Part A) . Name all pairs of similar triangles in the diagram

the answer is
triangle ABG
triangle ACF
triangle ADE

Part B)  Find the lengths of segment BG
we know that
AB/BG=AD/DE----------> BG=(AB*DE)/AD
DE=6 ft
BD=6.32 ft
AB=BC=CD=6.32/2----------> 3.16 ft
AD=6.32+3.16------> AD=9.48 ft
BG=(AB*DE)/AD---------> 3.16*6/9.48----------> BG=2 ft

the answer Part B) is 
BG=2 ft

Part C)  Find the lengths of segment CF
we know that
AC/CF=AD/DE----------> CF=(AC*DE)/AD
AC=6.32 ft
DE=6 ft
AD=9.48 ft
CF=(AC*DE)/AD---------> 6.32*6/9.48----------> CF=4 ft

the answer Part C) is 
CF=4 ft

Ujjg