contestada

C is the midpoint of AB, D is the midpoint of AC, E is the midpoint of AD, F is the midpoint of ED, G is the midpoint of EF, and H is the midpoint of DB. If DC=56, what is GH?

Respuesta :

The length of Line GH of the given Line segment is gotten as; 105

How to solve division of Line Segments?

From the figure:

AD = DC = 56

Thus;

56 = AE + ED (because E is the mid point of AD)

Thus;

ED = AE = 56/2

ED = AE = 28

AE = 28 = EF + FD (F is the mid point of ED)

EF = FD = 28/2

EF = FD = 14  

EF = 14 = EG + GF (Because G is the mid point of EF)

EG = GF = 14/2

EG = GF = 7

AC  = DC + AD (D is the mid point of AC)

AC = 56 + 56 = 112

AC = BC  (C is the mid point of AB)

BC = CH + HB

So, AC = CH + HB (AC = BC)

BD = DH + BH (H is the mid point of BD)

DH = CH + DC (from the figure)

AC = CH  + CH + DC

112 = 2CH + 56

CH = 28

GH = GF + FD + DC + CH

GH = 7 + 14 + 56 + 28 = 105

Read more about Division of Line Segments at; https://brainly.com/question/4747771

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