Question

state Pythagoras theorem and prove it​

Answer 1

Answer:      

Explanation:

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.

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 thoeroem is proved.

Answer 2

Answer:

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

Explanation:

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.