You can
put this solution on YOUR website! presumably these are all part of the same line.
you have the line of af equal to ab + bc + cd + de + ef
the line would look like this:
---------------------------------------------------
a b c d e f
you are given that the line segment ac is equal to df.
you are also given that the line segment bc is equal to ef
that would look like this:
---------------------------------------------------------
a b c d e f
--------------------- ---------------------
a c equals d f
----------- -----------
b c equals e f
you are given that ac = df
you know that ac = ab + bc
you know that df = de + ef
this means that ab + bc = de + ef by substitution of equals.
you are given that bc = ef
this means that you can substitute bc for ef or you can substitute ef for bc in any equation.
the equation of interest is:
ab + bc = de + ef
substitute bc for ef to get:
ab + bc = de + bc
subtract bc from both sides of this equation to get:
ab = de
you can do this because of the basic algebraic property that says:
if a + c = b + c then a = b
this follows from the fact that if you subtract the same quantity from both sides of an equality, then the equality is preserved.
you are left with ab = de which is what you wanted to prove so you are done.
