5.5 the triangle inequality ink.notebook · 5.5 the triangle inequality ink.notebook 2 december 05,...
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5.5 The triangle inequality ink.notebook
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December 05, 2017
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5.5 The Triangle Inequality
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Lesson Objectives Standards Lesson Notes
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5.5 The Triangle Inequality
Lesson Objectives
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Lesson NotesStandards
After this lesson, you should be able to successfully apply The Triangle Inequality to prove if the sides form a triangle and find the range of the third side of the triangle.
5.5 The triangle inequality ink.notebook
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Lesson Objectives Standards Lesson Notes
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
G.CO.10 Prove theorems about triangles.
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
A B
Cab
c
Example: The measures of two sides of a triangle are 5 and 8. Find a range for the length of the third side.
By the Triangle Inequality Theorem, all three of the following inequalities must be true.
Therefore x must be between _____ and ______.
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Is it possible to form a triangle with the given side lengths? If not, explain why not.
1. 6, 9, 15 2. 8, 8, 8
4. 1.5, 2.5, 33. 4, 8, 16
Find the range for the measure of the third side of a triangle given the measures of two sides.
6. 12 yd and 18 yd5. 1 cm and 6 cm
8. 82 cm and 1 m7. 1.5 ft and 5.5 ft
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9. GARDENING Hank has 4 lengths of wood from which he plans to make a border for a triangularshaped herb garden. The lengths of the wood borders are 8 inches, 10 inches, 12 inches, and 18 inches. How many different triangular borders can Hank make?
PRACTICE
State if the three numbers can be the measures of the sides of a triangle.
1. 8, 10, 7 2. 9, 2, 10
3. 12, 7, 19 4. 6, 11, 13
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Two sides of a triangle have the following measure. Find the range of possible measures for the third side.
6. 9, 75. 9, 6
7. 6, 11 8. 6, 10
Order the sides of each triangle from shortest to longest.
9. 10.
Order the sides of each triangle from shortest to longest.
11. 12.Order the sides of each triangle from shortest to longest.
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Order the sides of each triangle from shortest to longest.Order the angles in each triangle from smallest to largest.17. 18.
Order the angles in each triangle from smallest to largest.
19. 20.Answers:
1. Yes 3. No, 12 + 7 = 19 5. 3 < x < 15 7. 5 < x < 17
17. ⁄C, ⁄A, ⁄B 19. ⁄M, ⁄K, ⁄L
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In the book, do pages 363 – 366, problems:
4, 6 – 16 EVENS, 52, 56 – 63
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