Question

state and prove the pythagoras theorem?​

Answer 1

Answer:

AC whole square equals to BC whole square addition sign AC whole square

thx

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Answer 2

6 Triangles

Pythagoras Theorem Statement

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangles have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say x, y and z) which has positive integer values, when squared are put into an equation, also called a Pythagorean triple.

Right Angle Triangle

Where

“a” is the perpendicular side,

“b” is the base,

“c” is the hypotenuse side.

According to the definition, the Pythagoras Theorem formula is given as:

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2

The side opposite to the right angle (90°) is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.

Pythagoras Theorem

Consider three squares of sides a,b,c mounted on the three sides of a triangle having the same sides as shown.

By Pythagoras Theorem –

Area of square A + Area of square B = Area of square C

Pythagoras Theorem Proof

Given: A right-angled triangle ABC.

To Prove- AC2 = AB2 + BC2

Pythagoras Theorem Proof

Proof: First, we have to drop a perpendicular BD onto the side AC

We know, △ADB ~ △ABC

Therefore, ADAB=ABAC (Condition for similarity)

Or, AB2 = AD × AC ……………………………..……..(1)

Also, △BDC ~△ABC

Therefore, CDBC=BCAC (Condition for similarity)

Or, BC2= CD × AC ……………………………………..(2)

Adding the equations (1) and (2) we get,

AB2 + BC2 = AD × AC + CD × AC

AB2 + BC2 = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC2 = AB2 + BC2

Hence, the Pythagorean thoerem is proved.

Note: Pythagorean theorem is only applicable to Right-Angled triangle.