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Inequalities in One Triangle

Inequalities in One Triangle. Objectives: Use triangle measurements to decide which side is longest or which angle is largest Apply the Triangle Inequality. Which side is larger, AC or BC?. B. BC > AC. 5. C. A. 3. Which angle is larger B or A?.  A >  B. B. 5. C. A. 3.

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Inequalities in One Triangle

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  1. Inequalities in One Triangle Objectives: Use triangle measurements to decide which side is longest or which angle is largest Apply the Triangle Inequality

  2. Which side is larger, AC or BC? B BC > AC 5 C A 3

  3. Which angle is larger B or A? A > B B 5 C A 3

  4. Theorem: Side Angle • If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

  5. Which angle is larger, D or F? F > D D 24 40 F E

  6. Which side is larger, DE or EF? DE > EF D 24 40 F E

  7. Ex. 1 Write the angles in order from least to greatest. C, A, B A 52 12 B 43 C

  8. Theorem: Angle Side • If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

  9. Ex. 2 Write sides in order from greatest to least. XZ, XY, YZ Y 128º 22º 30º X Z

  10. Darwin Australia Perth Sydney

  11. Theorem:Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles. 1 3 2 2  3 Which angle is larger 2 or 3? Which angle is larger 1 or 3? 1  3

  12. Constructing a Triangle Not every group of 3 segments can be used to form a triangle.

  13. How can you tell if it is possible for three sides to form a triangle? The 2 smaller sides must add up to be MORE THAN the largest side.

  14. Triangle Inequality Theorem The sum of the lengths of the two smaller sides must be greater than the length of the 3rd side. C B A

  15. Determine if the three numbers can be measures of the sides of a triangle. If no, explain. • 13, 28, 19 • 28, 96, 124 Yes Yes NO

  16. Finding Possible Side Lengths

  17. subtract add subtract add If two sides of a triangle have the following measures, find the range of possible measures of the third side. • 10, 7 b. 18 , 11 7 < x < 29 3 < x < 17 Remember: you can't have negative side lengths

  18. Practice p. 287 #1 – 23 odd (12 problems)

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