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Worksheet Triangle Inequalities, Study notes of Geometry

Worksheet Triangle Inequalities. Name. Decide whether each set of numbers is a triangle. ... 11) Write an inequality to represent your answer:______.

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2021/2022

Uploaded on 08/05/2022

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Worksheet Triangle Inequalities
Name ___________________
Decide whether each set of numbers is a triangle.
1) 15, 12, 9 2) 23, 16, 7
3) 20, 10, 9 4) 8.5, 6.5, 13.5
5) 47, 28, 70 6) 28, 41, 13
7) 5, 10, 15 8) 9, 40, 41
9) 12, 2.2, 14.3 10) 6,9, 16
The measures of two sides are given. Between what two numbers must the third side fall.
11) 9 and 15 11) Write an inequality to represent your answer:_____________
12) 11 and 20 12) Write an inequality to represent your answer:_____________
13) 23 and 14 13) Write an inequality to represent your answer:_____________
14) 5 and 8 14) Write an inequality to represent your answer:_____________
15) 15 and 18 15) Write an inequality to represent your answer:_____________
16) 22 and 34 16) Write an inequality to represent your answer:_____________
17) 47 and 71 17) Write an inequality to represent your answer:_____________
18) 21 and 47 18) Write an inequality to represent your answer:_____________
Name the largest and the smallest angle.
19) 20) 21)
List the angles of
ABC from the smallest to the largest.
22)
= = =
17, 21, 18
AB BC AC
23)
= = =
15, 16, 17
AB AC BC
A
C
B
5
6
7
D
F
E
5
4
3
G
J
H
5
5.1
5.03
pf2

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Worksheet Triangle Inequalities Name ___________________

Decide whether each set of numbers is a triangle.

  1. 15, 12, 9 2) 23, 16, 7
  2. 20, 10, 9 4) 8.5, 6.5, 13.
  3. 47, 28, 70 6) 28, 41, 13
  4. 5, 10, 15 8) 9, 40, 41
  5. 12, 2.2, 14.3 10) 6,9, 16 The measures of two sides are given. Between what two numbers must the third side fall.
  6. 9 and 15 11) Write an inequality to represent your answer:_____________
  7. 11 and 20 12) Write an inequality to represent your answer:_____________
  8. 23 and 14 13) Write an inequality to represent your answer:_____________
  9. 5 and 8 14) Write an inequality to represent your answer:_____________
  10. 15 and 18 15) Write an inequality to represent your answer:_____________
  11. 22 and 34 16) Write an inequality to represent your answer:_____________
  12. 47 and 71 17) Write an inequality to represent your answer:_____________
  13. 21 and 47 18) Write an inequality to represent your answer:_____________ Name the largest and the smallest angle.

List the angles of ∆ ABC from the smallest to the largest.

22) AB= 17, BC = 21, AC = 18 23) AB= 15, AC = 16, BC = 17

A

C B

5 6 7 D

F E

5 4

3 G

J 5 H 5.03^ 5.

List the sides in order, underline the side with the shortest length.

List the sides of ∆ ABC from the longest to shortest.

27) m ∠ A= 46 ,° m ∠ B = 30 ° 28) m ∠ C = 101 ,° m ∠B = 70 ° 29) m ∠ A= 59 ,° m ∠ C = 61 °

Find the value of x and list the sides ofindicated measures. (Hint: Find the angle measures first, then decide which sides are the longest) ∆ ABC in order from shortest to longest if the angles have the

30) m ∠A = ( 9 x+ 29 )° , m ∠B = ( 93 − 5 x)° , and m ∠C = ( 10 x+ 2 )°.

31) m ∠A = ( 9 x− 4 )° , m ∠B = ( 4 x− 16 )° , and m ∠C = ( 68 − 2 x)°.

32) m ∠A = ( 12 x− 9 )° , m ∠B = ( 62 − 3 x)° , and m ∠C = ( 16 x+ 2 )°.

33) m ∠A = ( 5 x+ 2 )° , m ∠B = ( 6 x− 10 )° , and m ∠C = ( x+ 20 )°.

34) m ∠A = ( 10 x)° , m ∠B = ( 5 x− 17 )° , and m ∠C = ( 7 x− 1 )°.

Answer the following questions.

35) Draw∆∆∆∆ DEA with a median EG. 36) Draw∆∆∆∆ JKH with an altitude JP.

  1. Find the value of x.

C

A B 70 °^47 °

E

D F

30 ° 125 ° 25 ° A

B 65 ° (^40) ° C

T O A

S^ SO^ is an altitude of∆∆∆∆^ SAT

(((( 4 x^ −−−−^6 ))))°°°°