Question

Using the side-splitter theorem, which segment length would complete the proportion?

Answer 1

Answer:

C. GJ

Step-by-step explanation:

The side-splitter theorem states that "if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally".

Based on this theorem, which an elaborate the following proportion

$\frac{GH}{GJ}=\frac{HE}{JF}$

Therefore, the segment that completes the proportion is GJ, because it must be used according to the theorem.

Answer 2

Answer:

B. JH

Step-by-step explanation:

Side-splitter theorem states that if a line is parallel to one of the sides of a triangle and intersects two other sides, then it divides the two other sides in equal proportion.

As per the given diagram,

We see line $JH$ is such a line which is parallel to side $EF$ of $\triangle GEF$.

Thus it divides $GE \ and \ GF$ in equal proportion as below.

$\frac{GH}{HE}=\frac{GJ}{JF}$

Thus $JH$ would complete the proportion.