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The Triangle Inequality Chapter 5.5

"Learning is like rowing upstream: not to advance is to drop back." Chinese Proverb. The Triangle Inequality Chapter 5.5.

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The Triangle Inequality Chapter 5.5

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  1. "Learning is like rowing upstream: not to advance is to drop back." Chinese Proverb The Triangle Inequality Chapter 5.5 Check.4.13Locate, describe, and draw a locus in a plane or space (e.g., fixed distance from a point on a plane, fixed distance from a point in space, fixed distance from a line, equidistant from two points, equidistant from two parallel lines, and equidistant from two intersecting lines). CLE 3108.1.6Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world. Check.4.11Use the triangle inequality theorems (e.g., Exterior Angle Inequality Theorem, Hinge Theorem, SSS Inequality Theorem, Triangle Inequality Theorem) to solve problems.

  2. Traveling by Plane • Traveling from Nashville to Minneapolis, for the shortest route, would you a. Go to Chicago then Minneapolis or b. Fly directly to Minneapolis Why "Learning is like rowing upstream: not to advance is to drop back." Chinese Proverb

  3. Traveling by Plane 362 Miles • Traveling from Nashville to Minneapolis, for the shortest route, would you a. Go to Chicago then Minneapolis 397+362=759 b. Fly directly to Minneapolis - 703 Why 703 Miles 397 Miles

  4. Traveling by Plane 362 Miles • Traveling from Nashville to Minneapolis, for the shortest route, would you a. Go to Chicago then Minneapolis 397+362=759 b. Fly directly to Minneapolis - 703 Why 703 Miles 397 Miles

  5. Triangle Inequality A 362 Miles • The Sum of the lengths of any two sides of a triangle is greater than the length of the third side • AB + BC > AC • BC + AC > AB • AC + AB > BC B 703 Miles 397 Miles C

  6. Identify the sides of a triangle 2, 4, 5 6, 8, 14 2 + 4 > 5 6 > 5 4 + 5 > 2 9 > 2 5 + 2 > 4 7 > 4 6 + 8 > 14 14 = 14 Not a triangle

  7. Determine the possible Side length • In XYZ, XY = 8 and XZ = 14 • Which measure cannot be YZ • 6 • 10 • 14 • 18 • XY + XZ > YZ • 8 + 14 > n • 22 > n Y Z X XY + YZ > XZ 8 + n > 14 n > 6 YZ + XZ >XY n + 14 > 8 n > -6 6 < n < 22 Answer is A

  8. Determine the possible Side length • In PQR, PQ=7.2 and QR = 5.2 • Which measure cannot be PR • 7 • 9 • 11 • 13 • PQ + QR > PR • 7.2 + 5.2 > n • 12.4 > n Q R P QR + PR > PQ 5.2 + n > 7.2 n > 2 PR + PQ >QR n + 7.2 > 5.2 n > -2 2 < n < 12.4 Answer is D

  9. Practice Assignment • Page 363, 6-16 even, 20

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