Question

If two lines are parallel to the same line,then they are parallel to eachotherGiven: a||c and b||c Prove a||b

Answer 1

Given: a||c and b||c

Prove a||b

we know that

if two lines are parallel, then their slopes are equal

that means

If a||c and b||c

then

ma=mc and mb=mc

so

by the transitive property

if ma=mc and mb=mc

then

ma=mb

the slopes of the lines a and b are equal

therefore

lines a and b are parallel