1. NAME : HOW ZHAO YIN (201420026)
HO QI YAN (201420009)
ONG RU YUN (201420030)
CLASS : FOUNDATION IN LIBERAL ARTS
MODULE : INTRODUCTION TO CRITICAL
THINKING
LECTURER : MS. DOT MACKENZIE
TERM : MAY 2014
DATE : 14 JULY 2014
TOPIC : PYTHAGORAS AND THE
PYTHAGOREAN THEOREM

2. PYTHAGORAS AND THE PYTHAGOREAN THEOREM
Illustration source: http://www.edb.utexas.edu/visionawards/petrosino/Media/Members/zhfbdzci/pythagoras1.gif
According to the UALR (2001),
“The Pythagorean theorem takes
its name from the ancient Greek
mathematician Pythagoras (569
B.C.-500 B.C.), who was perhaps
the first to offer a proof of the
theorem. But people had noticed
the special relationship between
the sides of a right triangle long
before Pythagoras.”

3. WHERE WAS
PYTHAGORAS
BORN?
Samo
s
Illustration source: http://intmstat.com/blog/2008/03/samos.jpg

4. WHAT IS PYTHAGOREAN
THEOREM?
According to the UALR (2001),
“The Pythagorean theorem states that the sum
of the squares of the lengths of the two other
sides of any right triangle will equal the square
of the length of the hypoteneuse, or, in
mathematical terms, for the triangle shown at
right,
a2 + b2 = c2.
Integers that satisfy the conditions
a2 + b2 = c2
are called "Pythagorean triples." ”

5. RIGHT-ANGLED TRIANGLE
Illustration source: http://www.mathopenref.com/images/triangle/hypotenuse.gif

6. Illustration source: http://www.mathsaccelerator.com/measurement/images/triangle-answer.gif
Right-Angled Triangle

7. HOW TO PROVE THE
EQUATION OF PYTHAGOREAN
THEOREM?
c
b
a
•There are four similar triangle with the rotation
of different angle which are 90°, 180°, and
270°.
•Area of triangle can be calculated by using
this formulae:
½ x a x b

8. •The four triangles
combined together to form
a square shape with a
square hole.
•The length of side of square
inside is a-b.
•The area of square inside is
(a-b)² or 2ab.
•The area of four triangles is
4(½ x a x b).
In the last, we get this formulae
c²= (a - b)² + 2ab
= a² - 2ab + b² + 2ab
= a² + b²

9. Illustration source: http://cdn.instructables.com/FN4/7VG4/GVZPOZOZ/FN47VG4GVZPOZOZ.MEDIUM.gif

10. Video source: http://www.youtube.com/watch?v=hTxqdyGjtsA&feature=related

11. EXERCISE 1:
Prove triangle X is a right-angled
triangle.
http://fc05.deviantart.net/fs70/f/2013/297/b/1/simple_background_by_biebersays-d6rnj7n.jpg

12. SOLUTIONS:
c2= b2+a2
Let AC2=AB2+BC2
AB2+BC2=82+152
AC2=64+225
=289
√AC2=√289
AC=17 cm
http://fc05.deviantart.net/fs70/f/2013/297/b/1/simple_background_by_biebersays-d6rnj7n.jpg

13. EXERCISE 2:
Assuming that triangle
Q is a right-angled
triangle, find the
length of side YZ.
http://hqwide.com/minimalistic-multicolor-gaussian-blur-simple-background-white-wallpaper-5602/

14. SOLUTIONS:
c2=b2+a2
Let ZY2=ZX2+XY2
ZX2+XY2=122+52
ZY2=144+25
=169
√ZY2=√169
ZY=13 cm
http://hqwide.com/minimalistic-multicolor-gaussian-blur-simple-background-white-wallpaper-5602/

15. (12, 35, 37)
http://hqwide.com/gaussian-blur-gradient-simple-background-blurred-colors-wallpaper-62699/

16. 122+352=144+1225
=1369
372=1369
122+352=372, therefore it has been proved that
12, 35, 37 are the sides of a Pythagorean
Triangle.
http://hqwide.com/gaussian-blur-gradient-simple-background-blurred-colors-wallpaper-62699/

17. http://www.wallsave.com/wallpaper/1920x1080/simple-light-gradient-211999.html

18. c2=b2+a2
52=b2+a2
Let a=b-1, b=a+1
52=b2+(b-1)2
52=b2+(b-1)(b-1)
52=b2+b2-b-b+1
25=2b2-2b+1
÷2 0=2b2-2b-24
0=b2-b-12
0=(b+3)(b-4)
Hypotenuse
b+3=0
b=-3
b should be
positive,
therefore
b=-3 is not
acceptable.
b-4=0
b=4 cm
a+1=b
a+1=4
a=3 cm
Therefore, lengths of
legs=3 cm, 4 cm
http://www.wallsave.com/wallpaper/1920x1080/simple-light-gradient-211999.html

19. REFERENCES
Bogomolny, A. (2012). Pythagorean Theorem. Retrieved July 9, 2014, from Cut
The Knot: http://www.cut-the-knot.org/pythagoras/.
Section 9.6 The Pythagorean Theorem. (2007). Retrieved July 10, 2014, from
2014, from Msenux Redwoods:
http://msenux.redwoods.edu/IntAlgText/chapter9/section6solutions.pdf.
Smoller, L. (2001, May). The History of Pythagorean Theorem. Retrieved July 10,
2014, from UALR College of Information Science and Systems Engineering:
http://ualr.edu/lasmoller/pythag.html.

21. http://www.ucsa.nl/wp-content/uploads/2012/10/Questions-and-Answers.jpeg