SEGMENT ADDITION POSTULATE PRACTICE QUESTIONS

Problem 1 :

Solve for x.

Solution :

By observing the figure.

RP = RQ + QP

x + 24 = 2x + 21 + 12

x + 24 = 2x + 33

x - 2x = 33 - 24

-x = 9

x = -9

So, the value of x is -9.

Problem 2 :

Solve for x.

Solution :

By observing the figure.

HF = HG + GF

x + 18 = 8 + 17 + 2x

x + 18 =  25 + 2x

x - 2x = 25 - 18

-x = 7

x = -7

So, the value of x is -7.

Problem 3 :

Solve for x.

Solution :

By observing the figure.

HG = IG - IH

HG = 22 - (2x - 10)

HG = 22 - 2x + 10

HG = 32 - 2x

JI = JH - IH

JI = 13 - (2x - 10)

JI = 13 - 2x + 10

JI = 23 - 2x

JG = JI + IH + HG

x  + 12 = 23 - 2x + 2x - 10 + 32 - 2x

 x + 12 =  45 - 2x

x + 2x = 45  - 12

3x = 33

x = 33/3

x = 11

So, the value of x is 11.

Problem 4 :

Solve for x.

Solution :

By observing the figure.

BE = BC + CD + DE

19 = 2x - 2 + 6 + x

19 = 3x + 4

3x = 19 - 4

3x = 15

x = 15/3

x = 5

So, the value of x is 5.

Problem 5 :

Solve for x.

Solution :

By observing the figure.

JI = JH - IH

JI = 8 - (2x - 19)

JI = 8 - 2x + 19

JI = 27 - 2x 

HG = IG - IH

HG = 6 - (2x - 19)

HG = 6 - 2x + 19

HG = 25 - 2x 

JG = JI + IH + HG

JG = 27 - 2x + 2x - 19 + 25 - 2x

2x - 7 = 33 - 2x

2x + 2x = 33 + 7

4x = 40

x = 40/4

x = 10

So, the value of x is 10.

Problem 6 :

Solve for x.

Solution :

By observing the figure.

ST = SU - TU

ST = 12 - 4

ST = 8

RU = RT + TU

RU = 31 + x + 4

RU = 35 + x

RU = RS + ST + TU

35 + x = 2x + 35 + 8 + 4

35 + x = 2x + 47

x - 2x = 47 - 35

-x = 12

x = -12

So, the value of x is -12.

Problem 7 :

Solve for x.

Solution :

By observing the figure.

VS = VU + UT + TS

5x - 2 = 5 + x - 2 + 7

5x - 2 = 10 + x

5x - x = 10 + 2

4x = 12

x = 12/4

x = 3

So, the value of x is 3.

Problem 8 :

Solve for x.

Solution :

By observing the figure.

KL = KM - LM

KL = x + 18 - (2x + 11)

KL = x + 18 - 2x - 11

KL = -x + 7

JM = JL + LM

JM = 13 + 2x + 11

JM = 24 + 2x

JM = JK + KL + LM

24 + 2x = 1 - x + 7 + 2x + 11

24 + 2x = x + 19

2x - x = 19 - 24

x = -5

So, the value of x is -5.