pythagorean theorem
play

Pythagorean Theorem In a right triangle with sides of length a and b - PowerPoint PPT Presentation

Jan 31, 2023 •497 likes •681 views

Pythagorean Theorem In a right triangle with sides of length a and b and hypotenuse c : a 2 + b 2 = c 2 MA202 Sections 5 & 401 Chapter 12-3 Slides Proving the Pythagorean Theorem MA202 Sections 5 & 401 Chapter 12-3 Slides Proving the

  1. Pythagorean Theorem In a right triangle with sides of length a and b and hypotenuse c : a 2 + b 2 = c 2 MA202 Sections 5 & 401 Chapter 12-3 Slides

  2. Proving the Pythagorean Theorem MA202 Sections 5 & 401 Chapter 12-3 Slides

  3. Proving the Pythagorean Theorem MA202 Sections 5 & 401 Chapter 12-3 Slides

  4. Example 12.16 MA202 Sections 5 & 401 Chapter 12-3 Slides

  5. Converse of the Pythagorean Theorem If you have a triangle with sides of length a , b , and c , where a 2 + b 2 = c 2 : then the triangle is a right triangle with hypotenuse the side of length c . MA202 Sections 5 & 401 Chapter 12-3 Slides

  6. Example 12.18 Determine if each of the following is a right triangle: 15 , 17 , 8 MA202 Sections 5 & 401 Chapter 12-3 Slides

  7. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 MA202 Sections 5 & 401 Chapter 12-3 Slides

  8. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ 10 , 5 , 5 3 MA202 Sections 5 & 401 Chapter 12-3 Slides

  9. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ √ ( Yes, 5 2 + (5 3) 2 = 25 + 75 = 100 = 10 2 ) 10 , 5 , 5 3 MA202 Sections 5 & 401 Chapter 12-3 Slides

  10. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ √ ( Yes, 5 2 + (5 3) 2 = 25 + 75 = 100 = 10 2 ) 10 , 5 , 5 3 5 , 11 , 12 MA202 Sections 5 & 401 Chapter 12-3 Slides

  11. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ √ ( Yes, 5 2 + (5 3) 2 = 25 + 75 = 100 = 10 2 ) 10 , 5 , 5 3 ( No, 5 2 + 11 2 = 25 + 121 = 146 � = 12 2 ) 5 , 11 , 12 MA202 Sections 5 & 401 Chapter 12-3 Slides

  12. Class Discussion In a square based right regular pyramid, the height off the square is measured from the center of the square. For some of the homework, remember the formulas for area from the previous section. MA202 Sections 5 & 401 Chapter 12-3 Slides

  13. Class Discussion Solve for x in the following figure: MA202 Sections 5 & 401 Chapter 12-3 Slides

  14. Class Discussion Solve for y in the following figure: MA202 Sections 5 & 401 Chapter 12-3 Slides

  15. Class Discussion Solve for x and y in the following figure: MA202 Sections 5 & 401 Chapter 12-3 Slides

  16. Class Discussion Find the area of the equilateral triangle: MA202 Sections 5 & 401 Chapter 12-3 Slides

  17. Homework Homework 7 (due 4/6/10): Section 12.3 # 2ac, 3, 4ab, 5, 6, 9, 32 Section 12.4 # 2b, 3c, 4d, 5d, 6ab, 19a, 23 MA202 Sections 5 & 401 Chapter 12-3 Slides

Recommend

Pythagorean Theorem Distance and Midpoints Slide 2 / 78 Table of Contents Pythagorean Theorem

Pythagorean Theorem Distance and Midpoints Slide 2 / 78 Table of Contents Pythagorean Theorem

Slide 1 / 78 Pythagorean Theorem Distance and Midpoints Slide 2 / 78 Table of Contents Pythagorean Theorem Click on a topic to go to that section Distance Formula Midpoints Slide 3 / 78 Pythagorean Theorem Click to return to the table

752 views • 26 slides
Pythagorean Theorem Distance Formula Distance and Midpoints Midpoints Slide 3 / 78 Slide 4 /

Pythagorean Theorem Distance Formula Distance and Midpoints Midpoints Slide 3 / 78 Slide 4 /

Slide 1 / 78 Slide 2 / 78 Table of Contents Pythagorean Theorem Click on a topic to go to that section Pythagorean Theorem Distance Formula Distance and Midpoints Midpoints Slide 3 / 78 Slide 4 / 78 Pythagorean Theorem Pythagorean

589 views • 13 slides
ABC above is a right triangle. The sides BC and AC are also known as the legs of the right

ABC above is a right triangle. The sides BC and AC are also known as the legs of the right

D AY 77 P ROOF OF THE P YTHAGOREAN THEOREM USING SIMILARITY I NTRODUCTION The Pythagorean theorem, named in honor of the Greek philosopher, Pythagoras of Samos, is one of the fundamental theorems in geometry. It is also referred to as the

806 views • 27 slides
Name_____________________________________Pd______Date_________________ Pythagorean Theorem Fix

Name_____________________________________Pd______Date_________________ Pythagorean Theorem Fix

What does it all mean??? What is this symbol ? __________________________ What does it mean or how is it used?

642 views • 18 slides
Pythagorean Theorem, Distance, and Midpoint Multiple Choice Questions Slide 2 / 31 1 What is the

Pythagorean Theorem, Distance, and Midpoint Multiple Choice Questions Slide 2 / 31 1 What is the

Slide 1 / 31 Pythagorean Theorem, Distance, and Midpoint Multiple Choice Questions Slide 2 / 31 1 What is the distance between the two points? A 3.61 B 3.92 C 13 D 5.7 Slide 3 / 31 2 What is the distance between (4,6) and (9,15)? A 106 B

571 views • 31 slides
More ( a, b, c ) s of Pythagorean triples Darryl McCullough University of Oklahoma March 3,

More ( a, b, c ) s of Pythagorean triples Darryl McCullough University of Oklahoma March 3,

More ( a, b, c ) s of Pythagorean triples Darryl McCullough University of Oklahoma March 3, 2003 1 A Pythagorean triple (PT) is an ordered triple ( a, b, c ) of positive integers such that a 2 + b 2 = c 2 . When a and b are relatively prime,

541 views • 19 slides
The ( a, b, c ) s of Pythagorean triples Darryl McCullough University of Oklahoma September

The ( a, b, c ) s of Pythagorean triples Darryl McCullough University of Oklahoma September

The ( a, b, c ) s of Pythagorean triples Darryl McCullough University of Oklahoma September 10, 2001 1 A Pythagorean triple (PT) is an ordered triple ( a, b, c ) of positive integers such that a 2 + b 2 = c 2 . When a and b are relatively

405 views • 23 slides
Recursive enumeration of Pythagorean triples Darryl McCullough University of Oklahoma March 28,

Recursive enumeration of Pythagorean triples Darryl McCullough University of Oklahoma March 28,

Recursive enumeration of Pythagorean triples Darryl McCullough University of Oklahoma March 28, 2003 1 A Pythagorean triple (PT) is an ordered triple ( a, b, c ) of positive integers such that a 2 + b 2 = c 2 . When a and b are relatively

627 views • 15 slides
31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the

31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the

31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the divergence theorem is to Greens theorem, for the flux. Both are 3D generalisations of 2D theorems. Theorem 31.1 (Stokes Theorem) . Let C be any closed

406 views • 3 slides
29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a

29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a

29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a closed surface bounding a solid D , oriented outwards. Let F be a vector field with continuous partial derivatives. Then F d

471 views • 3 slides
Towards a Natural Interval Main Reference Interpretation of Pythagorean and Complex Home Page

Towards a Natural Interval Main Reference Interpretation of Pythagorean and Complex Home Page

Formulation of the . . . Our Explanation Towards a Natural Interval Main Reference Interpretation of Pythagorean and Complex Home Page Title Page Degrees of Confidence Jose Perez, Eric Torres, and Vladik

201 views • 7 slides
Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over

Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over

Griffith University 3130CIT Theory of Computation (Based on slides by Harald Sndergaard of The University of Melbourne) Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over a finite

422 views • 17 slides
Pythagorean-Triple-Based Table Generation for Trigonometric Function Evaluation MetaLibm Project

Pythagorean-Triple-Based Table Generation for Trigonometric Function Evaluation MetaLibm Project

Pythagorean-Triple-Based Table Generation for Trigonometric Function Evaluation MetaLibm Project Annual Meeting2015 Hugues de Lassus Saint-Genis Advisors: David Defour and Guillaume Revy DALI project-team, University of Perpignan Via

953 views • 69 slides
PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks

PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks

PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks Theorem. Ingo Wegener, 2005 Computational Complexity, by Fu Yuxi PCP Theorem 1 / 119 S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof

1.53k views • 120 slides
On Theorem Proving for Program Checking Historical perspective and recent developments Maria

On Theorem Proving for Program Checking Historical perspective and recent developments Maria

Outline Introduction Where is theorem proving in program checking Inside theorem proving Big and little engines together: a new theorem proving style Decision procedures with speculative inferences Current and future challenges On Theorem

944 views • 69 slides
Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers Amnon Yekutieli

Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers Amnon Yekutieli

Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers Amnon Yekutieli Department of Mathematics Ben Gurion University email: amyekut@math.bgu.ac.il Notes available at http://www.math.bgu.ac.il/~amyekut/lectures written 7

1.4k views • 121 slides
The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are

The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are

The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are finite subsets of V such that V = Span ( G ) , |G| = n , L is linearly independent, and |L| = m . Then m n and there is a set H G , such that

468 views • 36 slides
Algebra, geometry, and Pythagorean triples Kaloyan Slavov Department of Mathematics ETH Z

Algebra, geometry, and Pythagorean triples Kaloyan Slavov Department of Mathematics ETH Z

Algebra, geometry, and Pythagorean triples Kaloyan Slavov Department of Mathematics ETH Z urich kaloyan.slavov@math.ethz.ch February 9, 2017 1 / 8 Basics 2 , 1 , 5 , 7 2 / 8 Basics 1 2 , 1 , 5 , 7 2 7 5 2 / 8

1.3k views • 87 slides
1 What is a Theorem Prover? What is a Theorem? Theorem: A formalizable statement which is

1 What is a Theorem Prover? What is a Theorem? Theorem: A formalizable statement which is

Prerequisites Course 2D1453, 2006-07 Undergraduate logic and discrete maths CS literacy Advanced Formal Methods Some functional programming experience useful The theorem prover Isabelle is programming in SML Some SML

644 views • 4 slides
22. Greens Theorem Theorem 22.1 (Greens Theorem) . If C is a positively oriented closed curve

22. Greens Theorem Theorem 22.1 (Greens Theorem) . If C is a positively oriented closed curve

22. Greens Theorem Theorem 22.1 (Greens Theorem) . If C is a positively oriented closed curve enclosing a region R then curl F d r = F d A. C R The circle in the centre of the integral sign is simply to emphasize

355 views • 4 slides
Generalized Intermediate Value Theorem Intermediate Value Theorem Theorem Intermediate Value

Generalized Intermediate Value Theorem Intermediate Value Theorem Theorem Intermediate Value

Generalized Intermediate Value Theorem Intermediate Value Theorem Theorem Intermediate Value Theorem Suppose f is continuous on [ a , b ] and let N be any number between f ( a ) and f ( b ) , where f ( a ) = f ( b ) . Then there exists a

59 views • 4 slides
Geometry Euclid of Alexandria The Founder of Geometry. He was a Greek mathematician, often

Geometry Euclid of Alexandria The Founder of Geometry. He was a Greek mathematician, often

Geometry Euclid of Alexandria The Founder of Geometry. He was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323283 BC) Pythagorean theorem Geometry

807 views • 66 slides
From Shang Gao Magic 15 If a 2 + b 2 = c 2 , then ( a , b , c ) is called to be a Background

From Shang Gao Magic 15 If a 2 + b 2 = c 2 , then ( a , b , c ) is called to be a Background

Magic 15 Magic 15 Background Two Square Theorem Galois Finite Fields Magic 15: A STORY OVER 380 YEARS Proofs of 2-Square Theorem Three Square Theorem Four Square Theorem Universal Polynomials Magic 15 Proof of Fifteen Theorem 15

1.31k views • 97 slides
Ch04. Maximum Theorem, Implicit Function Theorem and Envelope Theorem Ping Yu Faculty of

Ch04. Maximum Theorem, Implicit Function Theorem and Envelope Theorem Ping Yu Faculty of

Ch04. Maximum Theorem, Implicit Function Theorem and Envelope Theorem Ping Yu Faculty of Business and Economics The University of Hong Kong Ping Yu (HKU) MIFE 1 / 27 The Maximum Theorem 1 The Implicit Function Theorem 2 The Envelope

599 views • 28 slides

More recommend