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Teorema Pythagoras

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ANTHURIUM

Square and Square Root of a NumberThis theorem is closely related to squaring numbers. Square of a number is the result of the number multiple by the number itself. In the other words, a2 says as multiply a by itself two times. Consider the following examples of squaring number.

32 = 3 × 342 = 4 × 4

Square root ( or unsquaring ) of a ( notated as) is a not negative number ( or 0 and a positive number) that the square is equal to a. consider the following examples of square rooting numbers.

= 2 since 22 =4 and 2 is not a negative number = 0.25 since (0.25)2 is not a negative numberIf x2 = a and x ≥ 0 then = x

The Pythagorean Theorem

RIGHT TRIANGLESPythagoren Theorem is a theorem which is relacted with the right triangle. Do you still remember what a right triangle is?

Definition:A right triangle is a triangle which one of its angles is a right angle (a 90° angle)

A

BC

Side AC is called hipotenusa Side AB dan AC is called legs of

right angle (or legs)

SEGITIGA SIKU – SIKUTeorema Pythagoras sebuah teorema yang berhubungan dengan segitiga siku – siku. Masih ingatkah kamu pengertian segitiga siku – siku?

Definisi :Segitiga siku – siku adalah segitiga yang besar salah satu sudutnya 90°.

A

BC

Sisi AC dinamakan hipotenusa Sisi AB dan AC dinamakan sisi

siku - siku

C

D

BDetermine the hypotenuse and the legs of the right triangles below.

6 cm

6 cm

10 cm

B. Panjang Sisi Segitiga Siku-siku

Perhatikan gambar di samping! Pada sebuah segitiga siku-siku ABC dengan AB sebagai hipotenusanya berlaku hubungan c² = a² + b². Berdasarkan Teorema Phytagoras, dapat dirumuskan rumus-rumus berikut.•c² = a² + b² => c =

Berbagai hubungan yang ekuivalen tersebut sangat bermanfaat untuk mencari panjang salah satu sisi suatu segitiga siku-siku apabila panjang dua sisi yang lainnya sudah diketahui.

A

0 B C D E

a² = c² - b² => a =

, orc² = a² + b² => c =

, or

b² = c² - a² => b =

Principle of Phytagorean Theorem

WHAT IS PHTAGOREN THEOREM???? Consider the following the discussion.

Suppose you have four squares such as: The area of red square is 3 X 3 = 9 square units The area of green square is 4 X 4 = 16 square units The area of yellow square is 7 X 7 = 49 square units

If inside of the yellow square there is a purple square, how wide is the area of purple square??? To find the area of the purple square, you can subtracting the area of yellow square with the area of four yellow triangles, which are the hypotenuses are the slides of the purple square. You will find that the area of each yellow triangle is ½ X 3 X 4 = 6 square units. Thus, the area of square- the area of yellow square triangle is = 49-24=25 square units. In other words, the area of purple square = the area of red square+ the area of red square.

AC2=AB2+BC2

Phytagorean TheoremIn this right angle C then:C2=a2+b2

Prinsip Teorema Pythagoras

Teorema pythagorasPada segitiga siku-siku di C berlaku:C2=a2+b2

Seperti apakah bunyi teorema phytagoras itu???? Perhatikanlah uraian berikut.

Misalnya, kamu mempunyai empat persegi, yaitu sebagai berikut: Luas persegi merah adalah 3 X 3 = 9 satuan luas Luas persegi hijau adalah 4 X 4 = 16 satuan luas Luas persegi kuning adalah 7 X 7= 49 satuan luas

jika di dalam persegi kuning ada persegi ungu,maka berapa luas persegi ungu?????

Kamu cukup mengurangkan luas persegi kuning dengan empat segitiga yang terbebtuk oleh persegi kuning dan ungu. Kamu peroleh bahwa luas setiap segitiga kuning tersebut adalah ½ X 3 X 4 = 6 satuan luas. Jadi luas keempat segitiga kuning tersebut adalah 4 X 6 = 24 satuan luas. Dengan demikian luas persegi ungu adalah luas persegi ungu- luas empat segitiga kuning= 49-24=25 satuan luas. Dengan kata lain, luas persegi ungu= luas persegi merah + luas persegi hijau. AC2=AB2+BC

Panjang Sisi Berbagai Jenis Segitiga

Misalnya, sisi C adalah sisi yang terpanjang pada ∆CDE.

1. Jika a² + b² = c² maka ∆CDE merupakan segitiga siku – siku.

2. Jika a² + b² > c² maka ∆CDE merupakan segitiga lancip

3. Jika a² + b² < c² maka ∆ACDE merupakan segitiga tumpul

C

D

E

a

b

c

The Lengths Sides of Any Triangles

Suppose, side c is the longest side in a ∆CDE 1. If a² + b² = c² then ∆CDE is a

right rectangle2. If a² + b² = c² then ∆CDE is a

acute rectangle3. If a² + b² = c² then ∆CDE is a

obtuse rectangle

C

D

E

a

b

c

There are special triangles known, there a ringht triangle has 450 angel and a right triangle that has 600 angel.

A Right Triangel has 450 AngelA Right Triangel has 450 Angel is the ratio of lengths of sides of an right triangle ABC with c as the hypotenuse is 1 : 1:

A Right Triangel that Has 600 AngelThe ratio of lengths of sides of a right triangle ABC that has 600 angelwith c as the hypotenuse isa : b : c = 1 : : 2.

The Ratio of Some Special Right Trisngels

E. Pythagorean Theorem in Daily Life

The application of Phytagorean Theorem in the real life is commonly found. The step to solve the application problems related to Pytagorean Theorem can be seen in the chart at right.

Problem solving

Calculation Results

• Sketch the right triangle

• Identify the problem

Calculation

E. Teorema Pythagoras dalam Kehidupan

Teorema Pythegoras sering kamu temukan dalam keseharianmu. Langkah-langkah untuk menyelesaikan soal-soal terapan yang berhubungan dengan Teorema Pythagoras dapat kamu lihat pada diagram di samping.

Soal Terapan • Buat sketsagambar segitigasiku-sikunya

• Perumusan masalah

Hasil perhitungan Perhitungan