12-5 Bell Work 12-5 Bell Work (stopwatch, role, stamp, passback)(stopwatch, role, stamp, passback)

A triangle has sides of 10, 11, and A triangle has sides of 10, 11, and 12. Where is the smallest angle?12. Where is the smallest angle?

A triangle has an exterior angle D A triangle has an exterior angle D and two non-adjacent interior and two non-adjacent interior angles A and B. Write one angles A and B. Write one equation and two inequalities for equation and two inequalities for them. them.

Hello great studentsHello great students

Backpacks below you.Backpacks below you. I am going to drop the lowest score I am going to drop the lowest score

of the semester. of the semester. Show your work for credit on Fridays.Show your work for credit on Fridays. I am going to reduce homework to I am going to reduce homework to

one page per day, probably the “B” one page per day, probably the “B” page.page.

Review Yesterday’s Review Yesterday’s AssignmentAssignment

5.5 B or C Review.5.5 B or C Review.

Today’s AssignmentToday’s Assignment Choose 3 numbers that work to Choose 3 numbers that work to

create a triangle and repeat with 4 create a triangle and repeat with 4 other sets. other sets.

Choose a set of three numbers that Choose a set of three numbers that do not make a triangle. Repeat 4 do not make a triangle. Repeat 4 more times.more times.

Choose two numbers and Choose two numbers and determine what the range for the determine what the range for the third side is. Repeat 4 more times. third side is. Repeat 4 more times. Total=15Total=15

ObjectivesObjectives

Test a set of 3 numbers to see if Test a set of 3 numbers to see if those sides could make a triangle.those sides could make a triangle.

Write inequalities to determine Write inequalities to determine the range of sizes for a third side the range of sizes for a third side (or what are the limits to the (or what are the limits to the thirds side?).thirds side?).

VocabularyVocabulary

Inequality: A relationship between Inequality: A relationship between two quantities that is greater two quantities that is greater than, less than, greater than or than, less than, greater than or equal to or less than or equal to.equal to or less than or equal to.

Example: x is less than 4.Example: x is less than 4.

Triangle Inequality Triangle Inequality TheoremTheoremThe sum of the lengths of any two sides of The sum of the lengths of any two sides of

a triangle is greater than the length of a triangle is greater than the length of the third side.the third side.

In triangle ABC, In triangle ABC, AB + BC > AC andAB + BC > AC andAC + BC > AB andAC + BC > AB andAB + AC > BCAB + AC > BC

How many inequalities are above? How many inequalities are above? If any one of these statements is false, If any one of these statements is false,

can the three sides work as a triangle?can the three sides work as a triangle?

Are these three sides Are these three sides able to form a able to form a triangle?triangle? 2,3 and 4.2,3 and 4. 2 + 3 > 4 ? True2 + 3 > 4 ? True 2 + 4 > 6? False. You are done. 2 + 4 > 6? False. You are done.

These three numbers can’t form a These three numbers can’t form a triangle.triangle.

Choose three numbers, add two of Choose three numbers, add two of them and see if they are greater them and see if they are greater than the third. Repeat twice more.than the third. Repeat twice more.

More practice on the More practice on the triangle inequality triangle inequality theorem.theorem.Can a triangle be made of sides 10, Can a triangle be made of sides 10,

14 and 8?14 and 8?

Write the three inequalities please.Write the three inequalities please.

What if someone gave What if someone gave you 2 sides and asked you 2 sides and asked what the range of what the range of numbers the third could numbers the third could be?be?

Say you have 10 and 15 as the Say you have 10 and 15 as the sides.sides.

Let us call the third side S. The Let us call the third side S. The inequalities are:inequalities are:

10 + 15 > S and 10 + S > 1510 + 15 > S and 10 + S > 15

I will do this for you.I will do this for you.

Triangle Inequality Triangle Inequality Theorem PracticeTheorem Practice The sides are 8 and 5. You do The sides are 8 and 5. You do

this one. What are all the this one. What are all the possibilities the third side could possibilities the third side could be?be?

Write the inequalities. Solve Write the inequalities. Solve them.them.

Summarize the Main Summarize the Main Point of the triangle Point of the triangle inequality theoreminequality theorem

Triangle Inequality Triangle Inequality TheoremTheorem http://www.regentsprep.org/http://www.regentsprep.org/

Regents/math/geometry/math-Regents/math/geometry/math-GEOMETRY.htmGEOMETRY.htm

5.6 Indirect Proof and 5.6 Indirect Proof and inequalities in two inequalities in two trianglestriangles2 red one blue cards. Which do I 2 red one blue cards. Which do I

have?have?http://www.regentsprep.org/Regents/math/geometry/GP3b/indirectteacher.htm

Indirect ProofIndirect Proof

Objective 1: Read and Write an Objective 1: Read and Write an Indirect ProofIndirect Proof

VocabularyVocabulary

An indirect proof is when you An indirect proof is when you prove a statement is true by first prove a statement is true by first assuming that its opposite is true.assuming that its opposite is true.

Hopefully, assuming the opposite Hopefully, assuming the opposite is true leads to an impossibility, is true leads to an impossibility, which proves your original which proves your original statement.statement.

Huh???Huh???

How to write an How to write an indirect proofindirect proof http://www.regentsprep.org/Rege

nts/math/geometry/GP3b/indirectlesson.htm

See Ex 1 page 302See Ex 1 page 302

Indirect ProofsIndirect Proofs