By: Bagoes Darmawan, S.Pd
Consider the Following Statement! “For Every Right Triangle The area of the square on the hypotenuse 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) c2 = a2+b2 b2 = c2-a2 a2 = c2-b2 Mawan24.wordpress.com
Example: Consider the following figure! C 3 cm 4 cm A B The length of BC is BC2 = AB2 + AC2 BC2 = 42 + 32
BC2 = 16 + 9 BC2 = 25 BC = ďƒ–25 =5cm
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Acute triangle a
b
c If c2 < a2+b2
Right triangle a
c b If c2 = a2+b2
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Obtuse triangle a
c b If c2 > a2+b2
Example: Show the triangle whose sides have length of 5 cm, 6cm, and 7 cm is a right triangle! Answer: From that question, the longest side is 7cm, so c2 =72 =49 a2+b2 = 52 + 62 = 25+36 = 61 c2 < a2+b2 So, the triangle is not right triangle, the triangle is acute triangle
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Consider the following triangle! A From the following figure, we know 30° that ABC is right triangle with angle 300, 600, and 900. This is special triangle and we can determine all side of triangle with formula: 60° C BC in front of A= 30 B AB in front of C =60 AC in front of B =90, so AB = 3 x BC = x AC = 2x Mawan24.wordpress.com
Example1: Consider the following figure! A When the length of side of equilateral 60° triangle is 6cm, the height of triangle is .... 60° B 60° C Answer: From the question, we can draw C
C
60°
6 cm 60°
A 3 cm
30°
6 cm 60°
3cm
B
6 cm 60°
A 3 cm B
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So, the value of BC is ....
Example1: Consider the following figure! G 30°
8 cm
E 60° F The value of EF and EG is .... Answer: EF = x So, FG = x.3 EF= x EG = 2x EG=2x = FG = x.3 = 8
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Consider the following triangle! A From the following figure, we know that ABC is right triangle with angle 45° 450, 450, and 900. This is special triangle and we can determine all 45° side of triangle with formula: 0 B C BC in front of A= 45 AB in front of C =450 AC in front of B =900, so AB = x BC = x AC = 2x Mawan24.wordpress.com
Example1: Consider the following figure! A D 8 cm B C The area of square is .... Answer: AB = x AC = x2 = 8 BC = x x = AC = x2 x x
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The area is = ( )2 = 16.2 = 32 cm2
Determine the length of hypotenuse or legs from the following triangle! a. b. 30°
10 cm 25cm 60°
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 ! Mawan24.wordpress.com