Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two...

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Lesson 5.4 The Triangle Inequality

Transcript of Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two...

Page 1: Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

Lesson 5.4

The Triangle Inequality

Page 2: Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Page 3: Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

Triangle Inequality Theorem Problems Determine if the measures given could be the sides of a

triangle. 16, 17, 19

16 + 17 = 33 yes, the sum of the two smallest sides is larger than the third side

6, 9, 15

6 + 9 = 15 no, the sum of the two smallest sides is equal to the other side so it cannot be a triangle

Find the range for the measure of the third side given the measures of two sides. 7.5 and 12.1

12.1- 7.5 < x < 12.1 + 7.5

4.6 < x < 19.6 9 and 41

41-9 < x < 41 + 9

32 < x < 50

Page 4: Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

Determine whether it is possible to form a triangle with side lengths 5, 7, and 8.

Page 5: Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

Find the range for the measure of the third side of a triangle if two sides measure 4 and 13.

Page 6: Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR?

A 7

B 9

C 11

D 13


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