Prove the converse of the Pythagorean theorem based on this Proof of the Pythagorean Theorem. A detailed proof is much appreciated
Prove the converse of the Pythagorean theorem based on this Proof of the Pythagorean Theorem. A detailed proof is much appreciated
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Prove the converse of the Pythagorean theorem based on this Proof of the Pythagorean Theorem. A detailed proof is much appreciated.
![A New Proof of the Pythagorean Theorem
We refer the reader to the figure below. It follows that
bc
1
x b x c = 5
2
1
x a x A'D –→ A'D = -
2
ΔΑAC
a
The right triangles ABC and AEA' are similar. Hence,
A' E
c2
ΑΕ
b
Α'Α
АЕ
АЕ
A'E
ас
A'E =
b
АС
АВ
ВС
b
C
a
2bc
ΕΗ-Α'Η - A'E =
ас
a
b
The right triangles ABC and HEC are also similar. Thus
- CE = " × ( - ) = 26 -
a?
= 2b -
b
ЕН
СЕ
ЕН
СЕ
a
2bc
ас
AB
ВС
C
a
b
c2
+( 2b
a?
5)- a' = b° + c?.
AC = AE + EC → b :
D
E
C'
C
b
В
H
а
-Submitted by Nam Gu Heo, Korea National University of Education
http://dx.doi.org/10.4169/amer.math.monthly.122.5.451
MSC: Primary 51-01
May 2015]
A SIMPLE COMPUTATION OF 5(2k)
451](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07f0e63c-5052-4f6e-b91e-9777cfeacc6d%2F64cfee73-7a5a-4e49-9c25-04805b4053f3%2Fmxiivwc_processed.png&w=3840&q=75)
Transcribed Image Text:A New Proof of the Pythagorean Theorem
We refer the reader to the figure below. It follows that
bc
1
x b x c = 5
2
1
x a x A'D –→ A'D = -
2
ΔΑAC
a
The right triangles ABC and AEA' are similar. Hence,
A' E
c2
ΑΕ
b
Α'Α
АЕ
АЕ
A'E
ас
A'E =
b
АС
АВ
ВС
b
C
a
2bc
ΕΗ-Α'Η - A'E =
ас
a
b
The right triangles ABC and HEC are also similar. Thus
- CE = " × ( - ) = 26 -
a?
= 2b -
b
ЕН
СЕ
ЕН
СЕ
a
2bc
ас
AB
ВС
C
a
b
c2
+( 2b
a?
5)- a' = b° + c?.
AC = AE + EC → b :
D
E
C'
C
b
В
H
а
-Submitted by Nam Gu Heo, Korea National University of Education
http://dx.doi.org/10.4169/amer.math.monthly.122.5.451
MSC: Primary 51-01
May 2015]
A SIMPLE COMPUTATION OF 5(2k)
451
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
