Question

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Proves the

↪️ Pythagoras theorem

( with diagram )
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Answer 1

First, we need to find the area of the trapezoid by using the area formula of the trapezoid.

A=(1/2)h(b1+b2) area of a trapezoid

In the above diagram, h=a+b, b1=a, and b2=b.

A=(1/2)(a+b)(a+b)

=(1/2)(a^2+2ab+b^2).

Now, let's find the area of the trapezoid by summing the area of the three right triangles.

The area of the yellow triangle is

A=1/2(ba).

The area of the red triangle is

A=1/2(c^2).

The area of the blue triangle is

A= 1/2(ab).

The sum of the area of the triangles is

1/2(ba) + 1/2(c^2) + 1/2(ab) = 1/2(ba + c^2 + ab) = 1/2(2ab + c^2).

Since, this area is equal to the area of the trapezoid we have the following relation:

(1/2)(a^2 + 2ab + b^2) = (1/2)(2ab + c^2).

Multiplying both sides by 2 and subtracting 2ab from both sides we get

a2. + b2. = c2

concluding the proof.

Answer 2

____________________________________↓↓↓↓↓

→Given :- We are given a right triangle ABC right angled at B .

→ Prove that :- AC² = AB² + BC²

→ Construction :- We draw BD perpendicular on AC .

→ Proof:- ∆ADB ≈ ∆ABC

So, AD/AB = AB/AC ..

or AD . AC = AB² .......(1)

Also,. ∆ BDC ≈ ∆ABC

So, CD/BC = BC/AC

or CD . AC = BC² .......(2)

Adding (1) & (2) ,

AD . AC + CD . AC = AB² + BC²

or , AC (AD + CD ) = AB² + BC²

or, AC . AC = AB² + BC²

or,. AC² = AB² + BC² .....

Hence, it is proved ....