1. 12-5 Bell Work (stopwatch, role, stamp, passback) A triangle has sides of 10, 11, and 12. Where is the smallest angle? A triangle has sides of 10, 11, and 12. Where is the smallest angle? A triangle has an exterior angle D and two non-adjacent interior angles A and B. Write one equation and two inequalities for them. A triangle has an exterior angle D and two non-adjacent interior angles A and B. Write one equation and two inequalities for them.

2. Hello great students Backpacks below you. Backpacks below you. I am going to drop the lowest score of the semester. I am going to drop the lowest score of the semester. Show your work for credit on Fridays. Show your work for credit on Fridays. I am going to reduce homework to one page per day, probably the “B” page. I am going to reduce homework to one page per day, probably the “B” page.

3. Review Yesterday’s Assignment 5.5 B or C Review.

4. Today’s Assignment Choose 3 numbers that work to create a triangle and repeat with 4 other sets. Choose 3 numbers that work to create a triangle and repeat with 4 other sets. Choose a set of three numbers that do not make a triangle. Repeat 4 more times. Choose a set of three numbers that do not make a triangle. Repeat 4 more times. Choose two numbers and determine what the range for the third side is. Repeat 4 more times. Total=15 Choose two numbers and determine what the range for the third side is. Repeat 4 more times. Total=15

5. Objectives Test a set of 3 numbers to see if those sides could make a triangle. Test a set of 3 numbers to see if those sides could make a triangle. Write inequalities to determine the range of sizes for a third side (or what are the limits to the thirds side?). Write inequalities to determine the range of sizes for a third side (or what are the limits to the thirds side?).

6. Vocabulary Inequality: A relationship between two quantities that is greater than, less than, greater than or equal to or less than or equal to. Example: x is less than 4.

7. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. In triangle ABC, AB + BC > AC and AC + BC > AB and AB + AC > BC How many inequalities are above? If any one of these statements is false, can the three sides work as a triangle?

8. Are these three sides able to form a triangle? 2,3 and 4. 2,3 and 4. 2 + 3 > 4 ? True 2 + 3 > 4 ? True 2 + 4 > 6? False. You are done. These three numbers can’t form a triangle. 2 + 4 > 6? False. You are done. These three numbers can’t form a triangle. Choose three numbers, add two of them and see if they are greater than the third. Repeat twice more. Choose three numbers, add two of them and see if they are greater than the third. Repeat twice more.

9. More practice on the triangle inequality theorem. Can a triangle be made of sides 10, 14 and 8? Write the three inequalities please.

10. What if someone gave you 2 sides and asked what the range of numbers the third could be? Say you have 10 and 15 as the sides. Say you have 10 and 15 as the sides. Let us call the third side S. The inequalities are: Let us call the third side S. The inequalities are: 10 + 15 > S and 10 + S > 15 10 + 15 > S and 10 + S > 15 I will do this for you.

11. Triangle Inequality Theorem Practice The sides are 8 and 5. You do this one. What are all the possibilities the third side could be? The sides are 8 and 5. You do this one. What are all the possibilities the third side could be? Write the inequalities. Solve them. Write the inequalities. Solve them.

12. Summarize the Main Point of the triangle inequality theorem

13. Triangle Inequality Theorem http://www.regentsprep.org/Regents/ math/geometry/math-GEOMETRY.htm http://www.regentsprep.org/Regents/ math/geometry/math-GEOMETRY.htm

14. 5.6 Indirect Proof and inequalities in two triangles 2 red one blue cards. Which do I have? http://www.regentsprep.org/Regents/ math/geometry/GP3b/indirectteacher. htm http://www.regentsprep.org/Regents/ math/geometry/GP3b/indirectteacher. htm http://www.regentsprep.org/Regents/ math/geometry/GP3b/indirectteacher. htm

15. Indirect Proof Objective 1: Read and Write an Indirect Proof Objective 1: Read and Write an Indirect Proof

16. Vocabulary An indirect proof is when you prove a statement is true by first assuming that its opposite is true. An indirect proof is when you prove a statement is true by first assuming that its opposite is true. Hopefully, assuming the opposite is true leads to an impossibility, which proves your original statement. Hopefully, assuming the opposite is true leads to an impossibility, which proves your original statement. Huh??? Huh???

17. How to write an indirect proof http://www.regentsprep.org/Regents/ math/geometry/GP3b/indirectlesson.ht m http://www.regentsprep.org/Regents/ math/geometry/GP3b/indirectlesson.ht m http://www.regentsprep.org/Regents/ math/geometry/GP3b/indirectlesson.ht m http://www.regentsprep.org/Regents/ math/geometry/GP3b/indirectlesson.ht m See Ex 1 page 302 See Ex 1 page 302

18. Indirect Proofs