Question #3cf21

1 Answer
Jul 15, 2016

#CE=5.6#cm, and, #BC=3.2#cm.

Explanation:

Observe that line #AB || DE, &, BD# is a transverse.

#:. m/_ABC=m/_ABD=m/_BDE=m/_CDE#.........[Alternate Angles]

Also, #m/_ACB=m/_ECD#...........[Opposite Angles].

Thus, #DeltaABC ~~ DeltaEDC#, by the correspondence,
#ABC harr EDC#

Since the corresponding sides of similar #Delta# are proportionate, we have,

#(AB)/(ED)=(BC)/(DC)=(CA)/(CE) rArr 4/8=(BC)/6.4=2.8/(CE)#

# rArr BC=3.2, &, CE=5.6#