phytagorean theorem
Post on 13-Mar-2016
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By:By:Bagoes Darmawan, S.Pd
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.”
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From that statement, so
a (leg) c (hypotenuse)
b (leg)b (leg)
c2 = a2+b2
b2 = c2-a2
a2 = c2-b2
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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
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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
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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
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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°
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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 ....
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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 =
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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
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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
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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°
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