1 ct ppt how zhao yin ho qi yan ong ru yun pythagoras and the pythagorean theorem 2014
TRANSCRIPT
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
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.”
WHERE WAS PYTHAGORAS
BORN?
Samos
Illustration source: http://intmstat.com/blog/2008/03/samos.jpg
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." ”
RIGHT-ANGLED TRIANGLEIllustration source: http://www.mathopenref.com/images/triangle/hypotenuse.gif
Illustration source: http://www.mathsaccelerator.com/measurement/images/triangle-answer.gif
Right-Angled Triangle
HOW TO PROVE THE EQUATION OF PYTHAGOREAN
THEOREM?
cb
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
•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
Illustration source: http://cdn.instructables.com/FN4/7VG4/GVZPOZOZ/FN47VG4GVZPOZOZ.MEDIUM.gif
Video source: http://www.youtube.com/watch?v=hTxqdyGjtsA&feature=related
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
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
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/
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/
EXERCISE 3:State whether the given triangle is a Pythagorean Triple. Give a reason for
your answer.
(12, 35, 37)
http://hqwide.com/gaussian-blur-gradient-simple-background-blurred-colors-wallpaper-62699/
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.
SOLUTIONS:
http://hqwide.com/gaussian-blur-gradient-simple-background-blurred-colors-wallpaper-62699/
EXERCISE 4:
The legs of a right triangle
are consecutive positive
integers. The hypotenuse has
length 5 cm. What are the
lengths of the legs?
http://www.wallsave.com/wallpaper/1920x1080/simple-light-gradient-211999.html
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=-3b should be positive, therefore b=-3 is not acceptable.
b-4=0 b=4 cma+1=ba+1=4 a=3 cm
Therefore, lengths of legs=3 cm, 4 cm
http://www.wallsave.com/wallpaper/1920x1080/simple-light-gradient-211999.html
SOLUTIONS:
REFERENCESBogomolny, 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 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.
ThanksFor
Listening
http://www.ucsa.nl/wp-content/uploads/2012/10/Questions-and-Answers.jpeg
THEEND