Question

garaphe
$x2 + y2$
​

Answer 1

Answer:

A right angled triangle.

To Prove:

Square of hypotenuse is equal to the sum of the squares of other two sides.

Construction:

Draw BD ⟂ AC

Proof: Let in a right angled (∠ABC is 90°) triangle ABC.

AC = Hypotenuse

AB and BC = Other sides

We have to prove AC² = AB² + BC²

Now, in ∆ADB and ∆ABC we have

∠A = ∠A {common}

∠ADB = ∠ABC {90° each}

∴ ∆ADB ~ ∆ABC by AA similarity.

\implies{\rm }⟹ AD/AB = AB/AC

\implies{\rm }⟹ AD(AC) = AB(AB)

\implies{\rm }⟹ AD(AC) = AB²......(1)

Now, in ∆BDC and ∆ABC we have

∠C = ∠C {common}

∠BDC = ∠ABC {90° each}

∴ ∆BDC ~ ∆ABC by AA similarity.

\implies{\rm }⟹ DC/BC = BC/AC

\implies{\rm }⟹ DC(AC) = BC(BC)

\implies{\rm }⟹ DC(AC) = BC².....(2)

Adding equation (1) and (2) we got

➮ AD(AC) + DC(AC) = AB² + BC²

➮ (AD + DC)AC = AB² + BC²

➮ AC(AC) = AB² + BC²

➮ AC² = AB² + BC²

\large\bold{\texttt {Proved }}Proved