Geometry WorksheetInequalities in One Triangle

Name---------------------------------Date Period. _

In exercises 1-10, the lengths of two sides of a triangle are given. First, write an inequality to describe allpossible values for x, the length of the third side of the triangle. Then, if domain of x is limited to the set

{!,1,4, 7, 9.3, 14, 19 }, list all possible values for x.2

1. 7,8 IL'Jt~/S- 5. 10,10 O"1(~;ao 8.t.'1/7, '1.3,14] 1 1 fY~III"I,,9.JJI'/,19J

2. 5,5 0 ~"~/O 6. 6-, 4- ~")CG a~ 9.[~II,l//7/tj·3j 531443 (£I,7,'.3}3. 1,8 1"1(49 pS 7.. , . 10.

4. 3,6 3LIV~Ji <~, 2 .7~1£4.'1.s",.. (.-J,7J [f

J'II"".33

11. If the lengths of two sides ofa triangle are 9 and 15, between what two numbers does the length of the thirdside lie? , c: It ~ .;2 4

12. If the lengths of two sides of a triangle are 3 and 7, then the length of the third side must be less than ~.

13. The lengths of two sides ofa triangle are 7 and 10. Between what two numbers does the third side lie?3L.1C4/7

14. The length of a leg of an isosceles triangle is 9. Between what two numbers does the length of the third sidelie? 0 ~ jl c: /8

15. Each leg of an isosceles triangle has length 12. Between what two numbers does the length ofthe base lie?0" ~~d."

In exercises 16-24, state whether it is possible for a triangle to exist with sides of the given lengths.

3.9,2.3

2! 5~2' 25, 11

4~~,g E~7j

, L ~ '/~ t 7, 9. JJI.f j

16. 6,11,4 Nt>17. 9,9, 10 floss;"'.

18. 8, 15, 7 Nf

19. x,2x,x (x>O) AlP 22. x,y,x+y (x andy> 0) NP20. 3x, 2x, 4x (x>O) PO$$,i,/e 23. x, y, x-y (x and y > 0) Nt>

21. x,x+3,x+4 (x>1)Pos-s-;'fc24. 2x,2x+2,4x+3 (x>O) PDss;"/c..

25. In ~C, mLA = 40 and mLACB = 110, what is the longest side of ~C? A6

26. What angle is the laraest in M>QR?

~ LI.-p 5 R

27. What side is the short~t in MBC?

A 60c

28. What side in a right triangle is the longest? Side "I'f~s; 'fe rijlt'" ~~ t-e: ( h,,,_+e nuse.)A B

-Be.

29. If AC > CX, and BX > BD, ~which angle is larger, Ll or~

c o

30. IfmLVRT = 120 and mLS > mLT, thenthe longest side of ARST is E x > I~o-x

01)(:::"0)C).,"OR Sv

31. In MBC, if AB =BC, mLl = 6x + 2and mL2 = 8x - 20, find mLB.

otn L8;: "t./

o('8 Bb'X+.;'l. = HIx -2-d

- 2.x = -l.z..)( =" "

32. Which side is the longest?the shortest?

~G t./' H

5$0

6iI--GXlfl!33. Which side is the longest? .~

the shortest? EFD

~FE 11~

~s34. Which side is the longest? 51.>

the shortest? ~o1./0

W

5x +-3+' K-}' + 102..: I go

11K + 103:: {eo111C= 77

)(~7

If the sides of a triangle have the following lengths, find all possible values for x.

35. AB = 2x + 5, BC = 3x - 2, AC = 4x - 8

6,)(-3 ~3J(-2.

3)(' ~ I)( ~ ~

7K -/0 » .;z~+.s-

S-J(~ IS'X~3

36. PQ = 3x, QR = 4x -7, PR = 2x + 9

7X;-7~~~+'T

Sl( ~ 16

X ~ "Is

, )(-1 il ~ 3K

3)(~-.:t

lc ~-~