Section 5-5 Inequalities for One Triangle

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The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

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Presentation transcript:

Section 5-5 Inequalities for One Triangle Integrated Math 3 Section 5-5 Inequalities for One Triangle

Example: Ordering Triangle Side Lengths and Angle Measures Write the angles in order from smallest to largest. The shortest side is , so the smallest angle is F. The longest side is , so the largest angle is G. The angles from smallest to largest are F, H and G.

Example: Ordering Triangle Side Lengths and Angle Measures Write the sides in order from shortest to longest. mR = 180° – (60° + 72°) = 48° The smallest angle is R, so the shortest side is . The largest angle is Q, so the longest side is . The sides from shortest to longest are

Example : Write the angles in order from smallest to largest. The shortest side is , so the smallest angle is B. The longest side is , so the largest angle is C. The angles from smallest to largest are B, A, and C.

If you know 2 of the sides you can give a range of what the third side length is. To get the lowest number the third side could be, subtract the two sides you know. To get the highest number the third side could be, add the two sides you know. Write your answer in this form: # < side < # Subtract 51 – 46 to get the low number and add 51 + 46 to get the high number. 5 < x < 97

Triangle Inequality Theorem Example: 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.

Triangle Inequality Theorem Example: 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.

Lesson Quiz: Part I 1. Write the angles in order from smallest to largest. 2. Write the sides in order from shortest to longest. C, B, A

Lesson Quiz: Part II 3. The lengths of two sides of a triangle are 17 cm and 12 cm. Find the range of possible lengths for the third side. 4. Tell whether a triangle can have sides with lengths 2.7, 3.5, and 9.8. Explain. 5 cm < x < 29 cm No; 2.7 + 3.5 is not greater than 9.8. 5. Ray wants to place a chair so it is 10 ft from his television set. Can the other two distances shown be 8 ft and 6 ft? Explain. Yes; the sum of any two lengths is greater than the third length.

Homework Section 5-5 p.146, #1-17 all