Inequality theorem (l4)

7
INEQUALITY THEOREM Module 6 Lesson 4

Transcript of Inequality theorem (l4)

Page 1: Inequality theorem (l4)

INEQUALITY THEOREM

Module 6 Lesson 4

Page 2: Inequality theorem (l4)

What is the triangle inequality theorem? ◦ According the regentsprep.org, “The sum of the lengths of any two sides of a

triangle must be greater than the third side.”

◦What does that mean? Add any 2 lengths of a triangle together and it will be greater than the 3rd side.

◦ http://www.regentsprep.org/regents/math/geometry/GP7/LTriIneq.htm

Page 3: Inequality theorem (l4)

So what does that mean?◦ If you are given two sides of a triangle, you can find the range of the 3rd side.

◦ If you have three numbers, you can determine if it would make a triangle or not.

Page 4: Inequality theorem (l4)

Try these…◦ Two sides of a triangle are 10 and 13. Find the range of possible measures of the 3rd

side.

◦Given the sides: 1, 2 and 3, does it form a triangle?

Page 5: Inequality theorem (l4)

Answers….◦ 3<x<23…subtract the sides to get 3. The 3rd side has to be greater than that. Add

the sides and the 3rd side must be less than that.

◦No, 1+2=3. The 2 sides added together must be greater than the 3rd. 3+2>1 and 3+1>2 but 1+2 isn’t greater than 3.

Page 6: Inequality theorem (l4)

Bonus question◦ This one is a most missed questions on the mastery assignment. Try it and check

your answer.

◦Write an inequality, describing x.

Page 7: Inequality theorem (l4)

Answer◦ Since the angle 86 is less than the right angle, the side across from 86 (3x+7) is

less than the side across from the right angle(5x+9).


Use the Exterior Angle Inequality Theorem to the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. measures less than 62/87,21 By the Exterior

Use the Exterior Angle Inequality Theorem to the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. measures less than 62/87,21 By the Exterior

MATHEMATICS CM - crashMATHS€¦ · Bernoulli’s inequality states that for all integers and every real number . (i) Using the binomial theorem on , prove Bernoulli’s inequality

MATHEMATICS CM - crashMATHS€¦ · Bernoulli’s inequality states that for all integers and every real number . (i) Using the binomial theorem on , prove Bernoulli’s inequality

Volume 2, Number 4, October 1989 - American ......1989/02/04  · 2.2. Theorem. An extension of Riesz's rearrangement inequality 2.3. Corollary. A rearrangement inequality for convex

Volume 2, Number 4, October 1989 - American ......1989/02/04  · 2.2. Theorem. An extension of Riesz's rearrangement inequality 2.3. Corollary. A rearrangement inequality for convex

Introductionarchive.ymsc.tsinghua.edu.cn/.../257/...Brunn-Minkowski_inequality.pdf · Therefore, Theorem 2 and Theorem 3 below are extensions of (1.4) ... Brunn-Minkowski inequality

Introductionarchive.ymsc.tsinghua.edu.cn/.../257/...Brunn-Minkowski_inequality.pdf · Therefore, Theorem 2 and Theorem 3 below are extensions of (1.4) ... Brunn-Minkowski inequality

Use the Exterior Angle Inequality Theorem to...Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. measures less than 62/87,21 By

Use the Exterior Angle Inequality Theorem to...Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. measures less than 62/87,21 By

ECE 8443 – Pattern Recognition Objectives: Jensen’s Inequality (Special Case) EM Theorem Proof EM Example – Missing Data Intro to Hidden Markov Models.

ECE 8443 – Pattern Recognition Objectives: Jensen’s Inequality (Special Case) EM Theorem Proof EM Example – Missing Data Intro to Hidden Markov Models.

Generalizations of Popoviciu’s inequalitygrinberg/Popoviciu.pdf · Generalizations of Popoviciu’s inequality ... Theorem 6 (Hardy, Littlewood, Polya). Let fbe a convex function

Generalizations of Popoviciu’s inequalitygrinberg/Popoviciu.pdf · Generalizations of Popoviciu’s inequality ... Theorem 6 (Hardy, Littlewood, Polya). Let fbe a convex function

McDiarmid’s Inequality - BGUatml192/wiki.files/ashish-mcdiarmid.pdf · McDiarmid’s Inequality • Theorem: Let be independent random variables all taking values in the set . Further,

McDiarmid’s Inequality - BGUatml192/wiki.files/ashish-mcdiarmid.pdf · McDiarmid’s Inequality • Theorem: Let be independent random variables all taking values in the set . Further,

Use the Exterior Angle Inequality Theorem toms-schmitz-geometry-honors.wikispaces.com/file/view/5-3...Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy

Use the Exterior Angle Inequality Theorem toms-schmitz-geometry-honors.wikispaces.com/file/view/5-3...Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy

Unit 4: Right Triangles Triangle Inequality Pythagorean Theorem and its Converse Trigonometry Inverse Trigonometry Solving Right Triangles.

Unit 4: Right Triangles Triangle Inequality Pythagorean Theorem and its Converse Trigonometry Inverse Trigonometry Solving Right Triangles.

Azuma-Hoeffding Inequality. Theorem 1.1. - … INEQUALITIES STEVEN P. LALLEY UNIVERSITY OF CHICAGO 1. THE MARTINGALE METHOD 1.1. Azuma-Hoeffding Inequality. Concentration inequalities

Azuma-Hoeffding Inequality. Theorem 1.1. - … INEQUALITIES STEVEN P. LALLEY UNIVERSITY OF CHICAGO 1. THE MARTINGALE METHOD 1.1. Azuma-Hoeffding Inequality. Concentration inequalities

Jeopardy Triangle Sides Triangle Inequality Hinge Theorem Converse of Hinge Theorem Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500.

Jeopardy Triangle Sides Triangle Inequality Hinge Theorem Converse of Hinge Theorem Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500.

5%2D4 Solving Compound · PDF fileSolve each compound inequality. ... The lowest speed you can go is ... (75< The Triangle Inequality Theorem states that the sum of the measures of

5%2D4 Solving Compound · PDF fileSolve each compound inequality. ... The lowest speed you can go is ... (75< The Triangle Inequality Theorem states that the sum of the measures of

ElEmEnts of · 2013. 8. 18. · 1.7 Limit Theorems 16 1.7.1 Markov Inequality 16 1.7.2 Chebyshev Inequality 17 1.7.3 Laws of Large Numbers 17 1.7.4 The Central Limit Theorem 18 Problems

ElEmEnts of · 2013. 8. 18. · 1.7 Limit Theorems 16 1.7.1 Markov Inequality 16 1.7.2 Chebyshev Inequality 17 1.7.3 Laws of Large Numbers 17 1.7.4 The Central Limit Theorem 18 Problems

§ 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem.

§ 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem.

Pythagorean Theorem Inequality and Pythagorean Triples

Pythagorean Theorem Inequality and Pythagorean Triples

The Prehistory of the Hardy Inequality - UM · PDF fileThe Prehistory of the Hardy Inequality Author(s): ... Toeplitz's method, ... "the proof of this theorem is much like that for

The Prehistory of the Hardy Inequality - UM · PDF fileThe Prehistory of the Hardy Inequality Author(s): ... Toeplitz's method, ... "the proof of this theorem is much like that for

55The Triangle Inequality Students will be able to use ... · GHLesson 55_notes.notebook November 03, 2015 Triangle Inequality Theorem is used to . . . (a) determine if three lengths

55The Triangle Inequality Students will be able to use ... · GHLesson 55_notes.notebook November 03, 2015 Triangle Inequality Theorem is used to . . . (a) determine if three lengths

ST. XAVIER’S COLLEGEstxavierstn.edu.in/dept/Physics/syllabuspg.pdf · matrices – Cayley Hamilton theorem - Eigen value problems -Schwartz inequality – Gram Schmidt orthogonalisation

ST. XAVIER’S COLLEGEstxavierstn.edu.in/dept/Physics/syllabuspg.pdf · matrices – Cayley Hamilton theorem - Eigen value problems -Schwartz inequality – Gram Schmidt orthogonalisation

Linearised Moser-Trudinger inequality · LINEARISED MOSER-TRUDINGER INEQUALITY MEELAE KIM As a limiting case of the Sobolev imbedding theorem, the Moser-Trudinger inequality was obtaine

Linearised Moser-Trudinger inequality · LINEARISED MOSER-TRUDINGER INEQUALITY MEELAE KIM As a limiting case of the Sobolev imbedding theorem, the Moser-Trudinger inequality was obtaine