Question

Prove that , in a triangle,if square of one side is equal to the sum of the squares of the other two sides , then the angles opposite the first side is a right angle​

Answer 1

Step-by-step explanation:

it is pythagoras therom proof

hypotenuse^2=adjacent^2+opposite^2

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 + BC

Answer 2

Answer:

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