Question

${\huge{\pink{\underline{\underline{ϙᴜᴇsᴛɪᴏɴ♪～}}}}}$

state and prove Pythagoras theorem. ​

Answer 1

Answer:

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 the right-angled triangle are called base, perpendicular and hypotenuse . Proof: ... ∠BAD = ∠BAC i.e. ∠A is common in both triangles.

hope it helps you

stay safe

Answer 2

Answer:

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 the right-angled triangle are called base, perpendicular and hypotenuse .

Step-by-step explanation:

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

Construction: Draw a perpendicular BD meeting AC at D.

We know, △ADB ~ △ABC

Therefore, AD/AB=AB/AC (corresponding sides of similar triangles)

Or, AB^2 = AD × AC ……………………………..……..(1)

Also, △BDC ~△ABC

Therefore, CD/BC=BC/AC (corresponding sides of similar triangles)

Or, BC^2= CD × AC ……………………………………..(2)

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

AB^2 + BC^2 = AD × AC + CD × AC

AB^2 + BC^2 = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC^2 = AB^2 + BC^2