Question

Match this median concurrent proof​

Answer 1

Answer:

E. (You always start with the given statement)

C.

A.

D.

B.

Step-by-step explanation:

The first line is given and therefore goes with E. Given.

The second line comes from the definition of median.

It bisects the opposite side from the vertex is being drawn from: So we have FA=FB, BE=EC, and CG=GA.

Second box goes with C.

Third line says FA/FB=1, BE/EC=1, and CG/GA=1.

How did they get this. It looks like they divided previous equation on both sides by right hand side's expression.

For example:

FA=FB

Divide both sides by FB you get:

FA/FB=FB/FB

FA/FB=1

So third line goes with A.

The fourth line is substitution property.  1=1(1)(1)=1(FA/FB)(BE/EC)(CG/GA). They replaced the 1's with what we had in the previous line.

Fifth line is Ceva's Theorem since it states that the FA:FB=BE:EC=CG:GA=1 implies the medians are concurrent.