Question 1153338

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those sides proportionally.

first:
{{{8/6=16/12}}}
{{{4/3=4/3}}}

or

{{{nq:qm=pr:rm}}}
{{{nq:(8+6)=pr:6}}}
{{{nq:14=pr:6}}}
{{{nq/pr=14/6}}}
{{{nq/pr=7/3}}}

{{{nm:nq=pm:pr}}}
{{{(12+16):nq=12:pr}}}
{{{28pr=12nq}}}
{{{nq/pr=28/12}}}
{{{nq/pr=7/3}}}

=> {{{nq}}} || {{{pr}}}