Question

Using the theorems and postulates prove that a||c and b||c equal a||b

Answer 1

we have that

if a||c

then

ma=mc ( if two lines are parallel, then their slopes are equal)

if b||c

then

mb=mc ( if two lines are parallel, then their slopes are equal)

therefore

Remember that

The Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z

Applying the transitive property

if ma=mc and mb=mc

then

ma=mb

that means

Line a and Line b are parallel lines because their slopes are equal