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Triangle Properties and Inequalities

Learn about triangle properties, including identifying lines and finding orthocenters, as well as solving inequalities and applying the Hinge Theorem.

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Triangle Properties and Inequalities

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  1. Bell work: Turn in when completed • For each triangle, identify the red line. Is it an altitude, median, angle bisector, perpendicular bisector, or none of the above?

  2. Finding the Orthocenter • Triangle ABC has vertices A(1,3), B(2,7), and C(6,3). What is its orthocenter? • Triangle DEF has vertices D(1,6), E(6, 1), and F(4,2). What is its orthocenter?

  3. 5-6: Inequalities in One Triangle

  4. List the angles of the triangles from smallest to largest

  5. Comparison Property of Inequality: If a=b+c, and c>0, then a>b

  6. Order the sides of the triangles from largest to smallest. Angle S = 24 Degrees Angle O = 130 Degrees

  7. Can a triangle have these side lengths? • 3, 7, 8 • 5, 10, 15

  8. What is the range of possible 3rd side lengths for these triangles? • 18, 23, x • 5, 16, x

  9. If a triangle has side lengths of 5 and 8, what are possible values for the 3rd side? • What if the sides were 4 and 7?

  10. 5-7: Inequalities in Two Triangles

  11. Using the Hinge Theorem • At which time are you farther from the base of the ride?

  12. Using its converse:What are the possible values for x?

  13. Homework: • 5.6, pages 328-329: 6, 11, 15, 19, 27 Honors: Add 32, 34 • 5.7, pages 336-337: 6, 10, 11, 15 Honors: Add 13, 17, 19a

  14. Quiz Retakes…last chance for quiz 2 and 3

  15. 5-6: For 11, 15, and 19, order the sides or angle from smallest-largest • For 27, find a range of possible values for the third side

  16. 10. When is the arm closer to the base? Justify your answer with the hinge theorem 5.7: 6. Compare the given sides with an inequality 11. Find the range of possible values for x

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