12
By: By: Bagoes Darmawan, S.Pd

Phytagorean Theorem

Tags:

Embed Size (px)

DESCRIPTION

Describe anything about triangle

Citation preview

Page 1: Phytagorean Theorem

By:By:Bagoes Darmawan, S.Pd

Page 2: Phytagorean Theorem

Consider the Following Statement!

“For Every Right TriangleThe area of the square on the hypotenuse equals the sum of the area of the square on equals the sum of the area of the square on the other two sides (legs)”“Luas persegi yang terletak pada hipotenusa sama dengan jumlah luas dari persegi yang terletak pada sisi-sisi segitiga yang lain.”

Mawan24.wordpress.com

Page 3: Phytagorean Theorem

From that statement, so

a (leg) c (hypotenuse)

b (leg)b (leg)

c2 = a2+b2

b2 = c2-a2

a2 = c2-b2

Mawan24.wordpress.com

Page 4: Phytagorean Theorem

Example:Consider the following figure!C

3 cm 4 cm

A B

The length of BC is BC2 = AB2 + AC2 BC2 = 16 + 9 BC2 = 42 + 32 BC2 = 25

BC = 25 =5cm

Mawan24.wordpress.com

Page 5: Phytagorean Theorem

Acute triangle Right triangle Obtuse triangle

a b a c a c

c b bIf c2 < a2+b2 If c2 = a2+b2 If c2 > a2+b2

Mawan24.wordpress.com

Page 6: Phytagorean Theorem

Example:Show the triangle whose sides have length of 5cm, 6cm, and 7 cm is a right triangle!Answer:From that question, the longest side is 7cm, soc2 =72 =49 c2 =72 =49 a2+b2 = 52 + 62 = 25+36 = 61 c2 < a2+b2

So, the triangle is not right triangle, the triangleis acute triangle

Mawan24.wordpress.com

Page 7: Phytagorean Theorem

Consider the following triangle!A From the following figure, we know

that ABC is right triangle with angle 300, 600, and 900. This is special triangle and we can determine all

30°

B C

triangle and we can determine all side of triangle with formula:BC in front of A= 30AB in front of C =60AC in front of B =90, soAB = 3 x BC = xAC = 2x

60°

Mawan24.wordpress.com

Page 8: Phytagorean Theorem

Example1:Consider the following figure!

A

B CAnswer:

60° 60°

60° When the length of side of equilateral triangle is 6cm, the height of triangle is ....

Answer:From the question, we can draw

C C

6 cm 6 cm 6 cm

A 3 cm 3cm B A 3 cm B

60° 60°

60°

60°

30°

So, the value of BC is ....

Mawan24.wordpress.com

Page 9: Phytagorean Theorem

Example1:Consider the following figure!

G

8 cm

E FThe value of EF and EG is ....Answer:

60°

30°

Answer:EF = x So, FG = x.3 EF= x EG = 2xFG = x.3 = 8 EG=2x =

Mawan24.wordpress.com

Page 10: Phytagorean Theorem

Consider the following triangle!A

From the following figure, we know that ABC is right triangle with angle 450, 450, and 900. This is special triangle and we can determine all

45°

B C

triangle and we can determine all side of triangle with formula:BC in front of A= 450

AB in front of C =450

AC in front of B =900, so

45°

AB = x BC = x AC = 2x

Mawan24.wordpress.com

Page 11: Phytagorean Theorem

Example1:Consider the following figure!A D

8 cm

B CThe area of square is ....Answer:Answer:AB = x AC = x2 = 8BC = x x = AC = x2

x

x

The area is = ( )2

= 16.2= 32 cm2

Mawan24.wordpress.com

Page 12: Phytagorean Theorem

Determine the length of hypotenuse or legs from the following triangle!a. b.

10 cm25cm

30°

25cm

10 cm The legs from triangle are 12 cm, 7 cm, and 5 cm.

Determine kinds of triangle The length of side of equilateral triangle is 18 cm.

Determine the height and the area of that triangle! Simplifying the root square of 1250 !

60°

Mawan24.wordpress.com


Probabilistically Checkable Proofs Theorem (PCP THEOREM)

Probabilistically Checkable Proofs Theorem (PCP THEOREM)

Documents
Thevenin’s theorem, Norton’s theorem and Superposition theorem for AC Circuits

Thevenin’s theorem, Norton’s theorem and Superposition theorem for AC Circuits

Documents
AB82 Thevenin’s Theorem Maximum Power Transfer Theorem ... · PDF fileAB82 Thevenin’s Theorem Maximum Power Transfer Theorem Analog Lab Experiment Board Ver. 1.0 QUALITY POLICY

AB82 Thevenin’s Theorem Maximum Power Transfer Theorem ... · PDF fileAB82 Thevenin’s Theorem Maximum Power Transfer Theorem Analog Lab Experiment Board Ver. 1.0 QUALITY POLICY

Documents
2 Greens Theorem Surface Integral Stokes Theorem

2 Greens Theorem Surface Integral Stokes Theorem

Documents
3. 4. 5. 8. Thevenin's theorem and Norton's theorem ...nagarjunauniversity.ac.in/ugcbcssyllabus/I B.Sc/Computer Maintenan… · Thevenin's theorem and Norton's theorem — verification

3. 4. 5. 8. Thevenin's theorem and Norton's theorem ...nagarjunauniversity.ac.in/ugcbcssyllabus/I B.Sc/Computer Maintenan… · Thevenin's theorem and Norton's theorem — verification

Documents
Network Theorems SUPERPOSITION THEOREM THÉVENIN’S THEOREM NORTON’S THEOREM MAXIMUM POWER TRANSFER THEOREM MILLMAN’S THEOREM SUBSTITUTION THEOREM RECIPROCITY

Network Theorems SUPERPOSITION THEOREM THÉVENIN’S THEOREM NORTON’S THEOREM MAXIMUM POWER TRANSFER THEOREM MILLMAN’S THEOREM SUBSTITUTION THEOREM RECIPROCITY

Documents
Mathematics of the Golden Section: from Euclid to ... · Theorem XIII, 5, Theorem XIII, 6, Theorem XIII, 8, Theorem XIII, 9 (all about DEMR), Theorem XIII, 17 (to inscribe a dodecahedron

Mathematics of the Golden Section: from Euclid to ... · Theorem XIII, 5, Theorem XIII, 6, Theorem XIII, 8, Theorem XIII, 9 (all about DEMR), Theorem XIII, 17 (to inscribe a dodecahedron

Documents
Euler’s partition theorem and the combinatorics of -sequencesEuler’s partition theorem. Theorem 1 (The ‘-Euler Theorem [9]) For integer ‘ ‚ 2, deflne the sequence fa(‘)

Euler’s partition theorem and the combinatorics of -sequencesEuler’s partition theorem. Theorem 1 (The ‘-Euler Theorem [9]) For integer ‘ ‚ 2, deflne the sequence fa(‘)

Documents
A UNIFYING IMPOSSIBILITY THEOREM · Recently, Vohra (2011) proves Arrow’s Impossibility Theorem, the Gibbard-Satterthwaite Theorem and the strategic candidacy impossibility theorem

A UNIFYING IMPOSSIBILITY THEOREM · Recently, Vohra (2011) proves Arrow’s Impossibility Theorem, the Gibbard-Satterthwaite Theorem and the strategic candidacy impossibility theorem

Documents
Factor Theorem & Rational Root Theorem - Hatboro€¦ · PPT file · Web viewRational Root Theorem * Rational Root Theorem: Suppose that a polynomial equation with integral coefficients

Factor Theorem & Rational Root Theorem - Hatboro€¦ · PPT file · Web viewRational Root Theorem * Rational Root Theorem: Suppose that a polynomial equation with integral coefficients

Documents
Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem

Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem

Documents
SLecture5 Rolle's Theorem and Mean Value Theorem

SLecture5 Rolle's Theorem and Mean Value Theorem

Documents
Central Limit Theorem · Central Limit Theorem 9.1 Central Limit Theorem for Bernoulli Trials The second fundamental theorem of probability is the Central Limit Theorem. This theoremsaysthatifSn

Central Limit Theorem · Central Limit Theorem 9.1 Central Limit Theorem for Bernoulli Trials The second fundamental theorem of probability is the Central Limit Theorem. This theoremsaysthatifSn

Documents
The Schema Theorem and Price’s Theorem

The Schema Theorem and Price’s Theorem

Documents
yvucdc.in · Web viewStatement and proofs of Superposition Theorem, Thevenin's Theorem, Norton's Theorem, Maximum Power transfer theorem, Milliman’s theorem and Reciprocity theorem

yvucdc.in · Web viewStatement and proofs of Superposition Theorem, Thevenin's Theorem, Norton's Theorem, Maximum Power transfer theorem, Milliman’s theorem and Reciprocity theorem

Documents
U.P. TECHNICAL UNIVERSITY LUCKNOW · 2015-10-28 · Superposition Theorem, Thevenin’s Theorem, Norton’s Theorem, Maximum Power Transfer Theorem (simple numerical problems). 9

U.P. TECHNICAL UNIVERSITY LUCKNOW · 2015-10-28 · Superposition Theorem, Thevenin’s Theorem, Norton’s Theorem, Maximum Power Transfer Theorem (simple numerical problems). 9

Documents
Word/Theorem Definition Example/Properties - … - 4 Square...Interior Angle Sum Theorem ... Word/Theorem Definition Example/Properties Trapezoid Interior Angle Sum Theorem ... "5,

Word/Theorem Definition Example/Properties - … - 4 Square...Interior Angle Sum Theorem ... Word/Theorem Definition Example/Properties Trapezoid Interior Angle Sum Theorem ... "5,

Documents
CHAPTER 3 NETWORK THEOREM. 2 NETWORK THEOREM Superposition Theorem Source Transformation Thevenin & Norton Equivalent

CHAPTER 3 NETWORK THEOREM. 2 NETWORK THEOREM Superposition Theorem Source Transformation Thevenin & Norton Equivalent

Documents
Theorem (Second Fundamental theorem of calculus)

Theorem (Second Fundamental theorem of calculus)

Documents
DUO - machine composition · 2017. 12. 7. · Between Phytagorean dreams and LaMettriean temptations 1. Categories and Varieties of Machine Composition systems ..... 146 2. Challenges

DUO - machine composition · 2017. 12. 7. · Between Phytagorean dreams and LaMettriean temptations 1. Categories and Varieties of Machine Composition systems ..... 146 2. Challenges

Documents
FACULTY OF ENGINEERING AND TECHNOLOGY REGULATIONS - 2015 · venin’s Theorem and Norton’s Theorem-Superposition Theorem-Maximum power transfer Theorem. UNIT – III RESONANCE AND

FACULTY OF ENGINEERING AND TECHNOLOGY REGULATIONS - 2015 · venin’s Theorem and Norton’s Theorem-Superposition Theorem-Maximum power transfer Theorem. UNIT – III RESONANCE AND

Documents
1 Chapter 12 Bond Selection. 2 Malkiel’s Interest Rate Theorems u Definition u Theorem 1 u Theorem 2 u Theorem 3 u Theorem 4 u Theorem 5

1 Chapter 12 Bond Selection. 2 Malkiel’s Interest Rate Theorems u Definition u Theorem 1 u Theorem 2 u Theorem 3 u Theorem 4 u Theorem 5

Documents
Course Plan Engineering Mathematics III (17MAT31) KLE Dr ......1. Verify Green’s theorem, Stokes theorem and Gauss divergence theorem. 2. Use Greens theorem, Stokes theorem and Divergence

Course Plan Engineering Mathematics III (17MAT31) KLE Dr ......1. Verify Green’s theorem, Stokes theorem and Gauss divergence theorem. 2. Use Greens theorem, Stokes theorem and Divergence

Documents
U (The Squeeze Theorem) · The Squeeze Theorem U) ‹ (The Squeeze Theorem) Min Eun Gi :

U (The Squeeze Theorem) · The Squeeze Theorem U) ‹ (The Squeeze Theorem) Min Eun Gi :

Documents
Chapter 13: Sequential Experiments & Bayes’ Theorem 1.(13.1) Partition Theorem 2.(13.2) Bayes’ Theorem 1.(13.1) Partition Theorem 2.(13.2) Bayes’ Theorem

Chapter 13: Sequential Experiments & Bayes’ Theorem 1.(13.1) Partition Theorem 2.(13.2) Bayes’ Theorem 1.(13.1) Partition Theorem 2.(13.2) Bayes’ Theorem

Documents
Pythagoras’ Theorem and Homer’s Ulysses. - uniurb.itisonomia.uniurb.it/vecchiaserie/2011Bomprezzi.pdf · Pythagoras’ Theorem and Homer’s Ulysses. ... Pythagoras‟ theorem

Pythagoras’ Theorem and Homer’s Ulysses. - uniurb.itisonomia.uniurb.it/vecchiaserie/2011Bomprezzi.pdf · Pythagoras’ Theorem and Homer’s Ulysses. ... Pythagoras‟ theorem

Documents
703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem… · 2020-02-10 · 703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem:

703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem… · 2020-02-10 · 703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem:

Documents
€¦ · Web viewNetwork theorems -Superposition theorem, Thevenin’s theorem, Norton’s theorem, Reciprocity theorem, Millman’s theorem, and Maximum power transfer theorem, application

€¦ · Web viewNetwork theorems -Superposition theorem, Thevenin’s theorem, Norton’s theorem, Reciprocity theorem, Millman’s theorem, and Maximum power transfer theorem, application

Documents
Scheme of Studies & Examination and Syllabi for B.Tech. in ... · Superposition theorem, Thevenin theorem, Norton theorem, Maximum power transfer theorem, Reciprocity theorem, Compensation

Scheme of Studies & Examination and Syllabi for B.Tech. in ... · Superposition theorem, Thevenin theorem, Norton theorem, Maximum power transfer theorem, Reciprocity theorem, Compensation

Documents
“fermat” and (“last theorem” or “great theorem”)

“fermat” and (“last theorem” or “great theorem”)

Documents