4.1: Triangle Inequality Theorem & Ordering Sides and Angles

4.3
Triangle Inequality Theorem
& Ordering Sides and Angles

​A triangle exists if: The sum of the 2 smaller sides is greater than the third side

​A triangle exists if: The sum of the 2 smaller sides is greater than the third side

​small + medium > large

​​sm + med > lg △✔

​​sm + med > lg △✔
​​sm + med = lg △X

​​sm + med > lg △✔
​​sm + med = lg △X
​​sm + med < lg △X

Multiple Choice

Determine if the following side lengths could form a triangles.

Prove your answer with an inequality.

#2) 3, 3, 7

• Yes

  3 + 3 > 7

• Yes

  3 + 3 < 7

• No

  3 + 3 < 7

• No

  3 + 3 > 7

Multiple Choice

Determine if the following side lengths could form a triangles.

Prove your answer with an inequality.

#4) 52, 37, 42

• Yes

  52 + 37 > 42

• Yes

  37 + 42 > 52

• No

  52 + 37 < 42

• No

  37 + 42 > 52

Drag and Drop

#5) 28, 50, 22

Do the side lengths form a triangle? ​ ​

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Prove your answer with an inequality ​

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No

22 + 28 = 50

Yes

22 + 28 > 50

28 + 50 > 22

22 + 28 < 50

Drag and Drop

#6) 6, 18, 14

Do the side lengths form a triangle? ​ ​ ​

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Prove your answer with an inequality ​

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Drag these tiles and drop them in the correct blank above

6 + 14 > 18

Yes

6 + 14 = 18

6 + 14 < 18

No

6 + 18 > 14

Drag and Drop

#7) 24, 12, 11

Do the side lengths form a triangle? ​ ​

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Prove your answer with an inequality ​

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Drag these tiles and drop them in the correct blank above

No

11 + 12 < 24

Yes

11 + 12 = 24

24 + 12 > 11

11 + 12 > 24

Drag and Drop

#8) 41, 7, 35

Do the side lengths form a triangle? ​ ​ ​

Placeholder

Prove your answer with an inequality ​

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Drag these tiles and drop them in the correct blank above

7 + 35 > 41

Yes

7 + 35 = 41

41 + 7 > 35

No

​smallest side

​largest side

​smallest side

​largest side

<A, <C, <B

Drag and Drop

Order the angle measures from least to greatest.

Small:​

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Medium:​ ​

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Large: ​ ​

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Drag these tiles and drop them in the correct blank above

Drag and Drop

Order the angle measures from greatest to least.

Large:​

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Medium:​ ​

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Small: ​ ​

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Drag these tiles and drop them in the correct blank above

Drag and Drop

Order the angle measures from greatest to least.

Large:​​

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Medium:​ ​

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Small:​ ​

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Drag these tiles and drop them in the correct blank above

​​ smallest angle

​​ largest angle

Drag and Drop

Order the angle measures from greatest to least.

Large:​​

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Medium:​ ​

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Small:​ ​

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Drag these tiles and drop them in the correct blank above

Drag and Drop

Order the side lengths from least to greatest:

Small:​

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Medium:​ ​

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Large:​ ​

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Drag these tiles and drop them in the correct blank above

​Go back to the front
#15 and #16

Multiple Select

Given two of the side lengths, check all possible lengths for the third side.

Select 3

#15) 15 ft and 27 ft

• 34

• 12

• 29

• 18

• 43

Multiple Select

Given two of the side lengths, check all possible lengths for the third side.

Select 2

#16) 45 cm and 9 cm

• 35

• 58

• 47

• 54

• 39