A midpoint is in the middle of a segment and splits the length in half.
GH=30
Practice makes perfect
Let's look at each midpoint and create a diagram to visualize the described situation.
C is the midpoint of AB
Since C is the midpoint, it is halfway in between A and B.
Using the same reasoning, we will place all of the listed midpoints in the middle of the given segments.
Given Description
Number line
D is the midpoint of AC
E is the midpoint of AD
F is the midpoint of ED
G is the midpoint of EF
H is the midpoint of DB
We are then told that the length DC is equal to 16. We can label this distance on our diagram and use our knowledge of the midpoints and the Segment Addition Postulate to find the length of GH.
Reasoning
Number line
DC=16
D is the midpoint of AC, so AD=DC.
AC=AD+DC, so AC=32. C is the midpoint of AB, so CB=32.
DB=DC+CB, so DB=48. H is the midpoint of DH, so DH= 24.
E is the midpoint of AD, so AE=ED=8.
F is the midpoint of ED, so FD=EF= 4. G is the midpoint of EF, so EG= GF= 2.
Finally, to find GH, we can use the Segment Addition Postulate to add GF, FD, and DH.
GF+ FD+ DH= GH ⇒ 2+ 4+ 24= 30
