Question

Can someone please explain how you do this. I would really appreciate it.

Answer 1

Check the picture below.

now, let's recall that running a segment from a midpoint across to a midpoint in a triangle, creates a midsegment, and a midsegment which is parallel to the "base" of the triangle, is always half of that base.

now, noticing the picture on the top-left triangle, we know those points are midpoints, so those in red are midsegments and therefore half the base, to make it short

IC = HE/2 = 7

JB = IC/2 = 3.5

now onto the top-right triangle, which is the same thing just basing itself on its other end

CG = AH/2 = 10

DF = CG/2 = 5

now, let's go to the  picture on the bottom-center

we  know that DG = 4, and since D and G are midpoints, DG is the midsegment of CEH thus

CH = 2DG = 8

likewise, on the green triangle ACH, the midsegment IB is half of the base CH, we know CH = 8, so IB = 4.