Question

After examining the figure shown here, Daniel determines that FG/TU= EF/ST wich theorem or collary allowed him to draw that conclusion?

A. Side-splitting theorem
B. two- transversal proportionality corollary
C.Proportional Altitudes theorem
D. Proportional Medians Theorem

Answer 1

C. Proportional Altitudes theorem :)

Answer 2

The Proportional Medians Theorem states:If two triangles are similar, then the ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.

A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.

It is given the two triangles are similar.FG and TU are the medians of the triangle .

By Proportional Medians Theorem ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.

So
`(FG)/(TU) =(EF)/(ST)`

Option D. Proportional Medians Theorem is the right answer.