PROBLEMS ON SEGMENT ADDITION POSTULATE

Segment addition postulate solve for x.

Problem 1 :

Find KL

Solution :

By observing the figure,

IL = 26

IJ = 9

JK = 11

KL = ?

IL = IJ + JK + KL

26 = 9 + 11 + KL

26 = 20 + KL

KL = 26 - 20

KL = 6

Problem 2 :

Find HJ

Solution :

By observing the figure,

GI = 7, GH = 2, IJ = 12

HJ = ?

HJ = HI + IJ

= (GI - GH) + IJ

= (7 - 2) + 12

= 5 + 12

HJ = 17

Problem 3 :

Find EC

Solution :

By observing the figure,

EB = 49, DC = 16, DB = 30

EC = ?

DB = DC + CB

EC = ED + DC

EC = 19 + 16

EC = 35

Problem 4 :

Find IK

Solution :

By observing the figure,

IL = 49, JK = 12, JL = 31

JL = JK + KL

IK = IJ + JK

IK = 18 + 12

IK = 30

Points A, B, and C are collinear. Point B is between A and C. Solve for x.

Problem 5 :

AC = 3x + 3, AB = -1 + 2x, and BC = 11. Find x.

Solution :

Given, AC = 3x + 3

AB = -1 + 2x

BC = 11

BC = AC - AB

11 = 3x + 3 - (-1 + 2x)

11 = 3x + 3 + 1 - 2x

11 = x + 4

x = 11 - 4

x = 7

Problem 6 :

AC = 22, BC = x + 14, and AB = x + 10. Find x.

Solution :

Given, AC = 22, BC = x + 14, AB = x + 10

AC = AB + BC

22 = x + 10 + x + 14

22 = 2x + 24

2x = 22 - 24

2x = -2

x = -2/2

x = -1

Problem 7 :

Solve for x.

Solution :

By observing the figure,

NK = 23, NM = x - 6, ML = 9

LK = 2x - 19

NK = NM + ML + LK

23 = (x - 6) + 9 + (2x - 19) 

23 = x - 6 + 9 + 2x - 19

23 = 3x - 16

3x = 23 + 16

3x = 39

x = 39/3

x = 13

Problem 8 :

Solve for x.

Solution :

By observing the figure,

SV = 4x - 29, ST = 13, TU = 6

UV = 2x - 18

SV = ST + TU + UV

4x - 29 = 13 + 6 + 2x - 18

4x - 29 = 19 + 2x - 18

4x - 2x = 19 - 18 + 29

2x = 30

x = 30/2

x = 15

Problem 9 :

Find DE

Solution :

By observing the figure.

DG = 33, DE = 3x - 28, EF = 3x - 30, FG = x

DG = DE + EF + FG

33 = 3x - 28 + 3x - 30 + x

Problem 10 :

Find EG

Solution :

By observing the figure,

EH = 26 + x

FG = 14 + x

FH = 12

EG = x + 23

EG = EF + FG

x + 23 = EF + 14 + x

x + 23 - 14 - x = EF

 EF = 9

EH = EF + FG + GH

x + 26 = 9 + 14 + x + GH

x  + 26 = 23 + x + GH

26 - 23 = GH

3 = GH

FH = FG + GH

12 = 14 + x + 3

12 = 17 + x

x = 12  -17

x = -5

EG = x + 23

= -5 + 23

EG = 18