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Worksheet by Kuta Software LLC

Geometry HW #7

Segment Addition Postulate Practice

Name___________________________________ ID: 1

Date________________ Period____©Z j2`0T1F4A bKPurtoaf tSIosfEtGwHavrae_ rLSLZCw._ B fAllOlO br\ixgBhQtcsz GrQefs\eerivke_dr.

Find the length indicated. Be sure to a) State the Segment Addition Postulate with variables, b)Substitute for the variables, c) Solve.

1) K ML

11

17

? 2) B DC

10

14

?

Solve for x. Be sure to a) State the Segment Addition Postulate with variables, b) Substitute forthe variables, c) Solve.

3) F DE

-12 + 2x x - 8

10

4) P RQ

3 2x + 22

x + 17

Find the length indicated. Be sure to a) State the Segment Addition Postulate with variables, b)Substitute for the variables, c) Solve.

5) Find DF D F

Ex + 7 7

4x + 2

6) Find CD B D

C2 2x - 6

x + 2

Solve for x. Be sure to a) State the Segment Addition Postulate with variables, b) Substitute forthe variables, c) Solve.

7) P SQ R

x - 4

18

2x - 6 1 8) D GE F

8 22x + 17

x + 20

Points A, B, C, and D are collinear and positioned in that order. Solve for x. Be sure to a) Statethe Segment Addition Postulate with variables, b) Substitute for the variables, c) Solve.

9) Find x if AC = 17, BD = 2x - 6, AD = x + 16, and BC = 6.

10) AD = 20, BC = 2, AB = x + 12, and CD = x + 12. Find x.

Segment Overlap Theorem

1) Fill in the blanks to complete The Segment Overlap Theorem: If P, Q, R and S are collinear, and in the order presented, then the following conditions must both be true:

THEN _____ _____IF PQ RS≅ ≅ & THEN _____ _____IF PR QS≅ ≅ Use figure 1 for questions 2 – 7: SHOW WORK by stating the Segment Overlap Theorem first with variables (you pick which version!), then substitute and solve algebraically.

2) If PQ = 8 and PR QS≅ , then RS = ______?

3) If PR = 12 and PQ RS≅ , then QS = ______?

4) If PQ = 2x – 5 and RS = 6x – 21, and PR QS≅ , then x = ___ and RS = ______?

5) If PR = 3x + 8 and QS = 6x – 13, and PQ RS≅ , then x = ___ and PR = ______?

These next problems require you to integrate both Segment Addition AND Segment Overlap to solve. Be sure to SHOW WORK!

6) If PQ = 5x + 2 and QS = 12x – 23, and QR = x + 5 and PQ RS≅ , then x = ___ and RS = ______?

7) If PQ = 3x + 30 & RS = 12x – 33, and QR = 2x + 5 and PR QS≅ , then x = ___ and QS = ______?

P Q R S

(figure 1)