Question

write Pythagoras theorem and prove it.​

Answer 1

Answer:

à^2+ b^2=c^2

Step-by-step explanation:

à^2= base side

b^2= perpendicular side

and, c^2 = hypotenuse side

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Answer 2

Answer:

In Right angle triangle , the square of hypotenuse is equal to the square of sum of other two sides

Given: A right-angled triangle ABC, right-angled at B.

To Prove- AC² = AB² + BC²

Construction: Draw a perpendicular BD meeting AC at D.

Pythagoras theorem Proof

Proof:

We know, △ADB ~ △ABC

Therefore, ADAB=ABAC (corresponding sides of similar triangles)

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

Also, △BDC ~△ABC

Therefore, CDBC=BCAC (corresponding sides of similar triangles)

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 theorem is proved.