It is given in the diagram that IJ = JH and IK = KG. Therefore, by the definition of a midpoint, we know that J and K are the midpoints of segments IH and IG respectively. Then, it can be concluded that JK is a midsegment by the definition of a midsegment. The Midsegment Theorem states that a midsegment connecting the midpoints of two sides of a triangle is parallel and half of the length of the third side. Thus, we know that JK is half of HG. Now, we can set up the following equation to solve for x:
