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Bell Ringer Activity: Pick your FAB FIVE….

Bell Ringer Activity: Pick your FAB FIVE…. This means pick the top 5 homework problems you want to work on. 5.5 Inequalities in Triangles. These triangles are NOT created equal………. .

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Bell Ringer Activity: Pick your FAB FIVE….

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  1. Bell Ringer Activity:Pick your FAB FIVE…. This means pick the top 5 homework problems you want to work on.

  2. 5.5 Inequalities in Triangles These triangles are NOT created equal……….

  3. First, let’s review solving inequalitiesRules for solving:We can add, subtract, multiply and divide both sides by bythe same value JUST LIKE when we solve equationsEXCEPTwhen we multiply or divide by a negative number. Try these:

  4. Corollary to the Triangle Exterior Angle Theorem • A corollary is a result of another theorem. • If m<2 = 50 degrees and m<3 = 63 degrees, what is the smallest degree measure that angle 1 could be?

  5. Applying the theorem to problems Show that m <2 > m <3: By the Isosceles Triangle Theorem, we know that <1 is congruent to <2. By the Triangle Exterior Angle Theorem, we know that m < 1 > m <3. Since m <1 = m <2, then we use substitution to show that m < 2 > m < 3.

  6. Applying the theorem to problems Show that m <OTY > m <3: Since m <OTY = m <4 + m <2, then m <OTY > m <2. We also know that m < 3 > m <2. So, since m <OTY > m <2 AND m < 2 > m <3 then m <OTY > m <3.

  7. Sample Problems

  8. If the length XZ > length YZ. Which is the larger angle, <X or <Y?

  9. Sample Problems • List the angles in order from least to greatest.

  10. Theorem 5-11 is the converse of Theorem 5-10 REMINDER: To find the converse of a conditional statement, switch the hypothesis and the conclusion.

  11. Apply Theorem 5-11 List the sides of the triangle from least to greatest.

  12. Experiment & Discussion • Take your pieces of paper and try to construct a triangle with them. What happens?

  13. Triangle Inequality Theorem

  14. How to apply the Triangle Inequality Theorem Can a triangle have sides with the given lengths? 3 ft, 7 ft, 8 ft Check to see that the sum of every pair of sides is greater than the third side: • 3 + 7 > 8 • 8 + 7 > 3 • 3 + 8 >7

  15. Finding possible side lengths given two side lengths • If a triangle has lengths of 8 ft and 12 ft, what are the possible lengths for a third side?

  16. Multiple Choice Practice

  17. Homework • Bring in your Triangle with the Center of Gravity indicated on one side. • Geometry 1st and 3rd: • Practice 5-5, pg 295 #36 • Geometry Honors: • Practice 5-5, evens, Enrichment 5-5, pg 295, #36

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