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Warm UP!

Warm UP!. Can any 3 side lengths make a triangle? Name the different kinds of triangles based on side length. Name the different kinds of triangles based on angle measure. Inequalities in One Triangle. Objectives:

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Warm UP!

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  1. Warm UP! Can any 3 side lengths make a triangle? Name the different kinds of triangles based on side length. Name the different kinds of triangles based on angle measure.

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

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

  4. 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.

  5. 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

  6. Determine if the three numbers can be measures of the sides of a triangle. If no, explain. • 25, 12, 17 • 9, 15, 6 Yes NO NO

  7. 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

  8. 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.

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

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

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

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

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

  14. 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.

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

  16. Darwin Australia Perth Sydney

  17. 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

  18. Marcus and his aunt are building a wooden planter for her flowers in the shape of a right triangle. He has calculated the longest board to be 17 feet. What would be the length of the other two boards? a. 13ft & 15ft b. 8ft & 15ft c. 3ft & 4ft d. 10ft & 15ft

  19. Questions? • The sides of a triangle are 12, 7, and x. Which of the following is a possible value for x? • a. 19 b. 5 c. 8 d. 21 • In triangle CAT, angle C is 54o and angle T is 36o. What is the longest side of the triangle? • a. CA b. CT c. AT d. cannot be determined

  20. Practice Worksheet: Front and Back Finish for Homework!

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