Question

prove that hypotenuse^2 = base^2+perpendicular^2​

Answer 1

Answer:

Step-by-step explanation:

NOW IN ΔABC AND ΔABD

 ∠BAD = ∠BAC

 ∠ABC = ∠ADB

BY AA SIMILARITY

ΔABC ≈ ΔABD

AB/AD = AC/AB

AB² = AC x AD..................(1)

NOW IN ΔABC AND ΔBDC

∠ABC = ∠BDC

∠BCD = ∠BCA

BY AA SIMILARITY

ΔABC ≈ ΔBDC

BC/CD = AC/BC

BC² = AC x CD..........(2)

ADD (1) AND (2)

AB² + BC² = AC x AD + AC x CD

AB² + BC² = AC(AD + CD)

AB² + BC² = AC x AC

AB² + BC² = AC²

HENCE THE SQUARE OF HYPOTENUSE IS EQUAL TO THE SUM OF THE SQUARE OF OTHER TWO SIDES