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55 Notes and answers Reg Geo.notebook
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Write indirect proofs.
Apply inequalities in one triangle.
Objectives
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55 Notes and answers Reg Geo.notebook
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Example 2A: Ordering Triangle Side Lengths and Angle Measures
Write the angles in order from smallest to largest.
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Example 2B: Ordering Triangle Side Lengths and Angle Measures
Write the sides in order from shortest to longest.
55 Notes and answers Reg Geo.notebook
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Check It Out! Example 2a
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Check It Out! Example 2b
55 Notes and answers Reg Geo.notebook
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A triangle is formed by three segments, but not every set of three segments can form a triangle.
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A certain relationship must exist among the lengths of three segments in order for them to form a triangle.
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Example 3A: Applying the Triangle Inequality Theorem
Tell whether a triangle can have sides with the given lengths. Explain.7, 10, 19
No—by the Triangle Inequality Theorem, a triangle cannot have these side lengths.
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Example 3B: Applying the Triangle Inequality Theorem
Tell whether a triangle can have sides with the given lengths. Explain.2.3, 3.1, 4.6
Yes—the sum of each pair of lengths is greater than the third length.
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55 Notes and answers Reg Geo.notebook
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February 26, 2016
Sep 248:59 PM
Check It Out! Example 3a
Tell whether a triangle can have sides with the given lengths. Explain.8, 13, 21
No—by the Triangle Inequality Theorem, a triangle cannot have these side lengths.
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Check It Out! Example 3b
Tell whether a triangle can have sides with the given lengths. Explain.6.2, 7, 9
Yes—the sum of each pair of lengths is greater than the third side.
ü ü ü
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Example 4: Finding Side Lengths
The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the third side.
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Check It Out! Example 5 The distance from San Marcos to Johnson City is 50 miles, and the distance from Seguin to San Marcos is 22 miles. What is the range of distances from Seguin to Johnson City?
Let x be the distance from Seguin to Johnson City.
x + 22 > 50x > 28
x + 50 > 22x > –28
22 + 50 > x
72 > x
28 < x < 72
The distance from Seguin to Johnson City is greater than 28 miles and less than 72 miles.
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Assignment(p. 348) 49, 1214, 2628
