Mathematics

Problem

Points

D

and

E

lie on sides

AB

and

AC

\triangle ABC

respectively. For which of the following sets of lengths is the line

DE

certain to be parallel to

BC

? a)

AD=3\,\text{cm},\; DB=6\,\text{cm},\; AE=8\,\text{cm},\; EC=4\,\text{cm}

AD=3\,\text{cm},\; DB=6\,\text{cm},\; AE=6\,\text{cm},\; EC=6\,\text{cm}

AD=3\,\text{cm},\; DB=5\,\text{cm},\; AE=4.5\,\text{cm},\; EC=7.5\,\text{cm}

AD=3\,\text{cm},\; DB=5\,\text{cm},\; AE=8\,\text{cm},\; EC=13\,\text{cm}