Question

If line JI is a midsegment of triangle FGH, find HG. All measurements in the diagram are in inches.

Answer 1

I hope this helps you



2x-3=x+2



X=5


HG=11x+5=11.5+5=60


JI=60/2=30

Answer 2

Answer:

Length of segment HG=60 inches.

Length of JI=30 inches.

Step-by-step explanation:

Given , if a line JI is a midsegment of triangle FGH.

Triangle midsegment theorem: It states that when a segment formed by joining of midpoints of any two sides of a triangle then it is parallel to III side of triangle and half of its length.

JI is the midsegment , J is the midpoint of side HF and I is the midpoint of GF

Therefore, we have

HJ=JF and GI=IF

2x-3=x+2

By subtracting property of equality

2x-x=2+3

x=5 ( by simplification)

Length of side HG= 11x+5

Length of side HG=$11\times 5+5=60$ inches.

By substituting the value of x

JI=$\frac{1}{2} HG$

By using theorem

JI=$\frac{1}{2} \times60=30$

JI=30 inches.