Question

ABC is an isosceles triangle right angled at C. prove that AB^2 = 2AC^2.​

Answer 1

Given:

• ABC is an isosceles triangle right angled at "C".

To proof:

• AB^2 = 2AC^2

Solution:

In ∆ABC,

∠C = 90°

AC = BC ( Given )

By using Pythagoras theorem,

→ AB^2 = AC^2 + CB^2

→ AB^2 = AC^2 + AC^2

→ AB^2 = 2AC^2

Hence,

• AB^2 = 2AC^2.

Answer 2

Given

• ABC is an isosceles triangle right angled at C.
• AC = AB

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To prove

• AB² = 2AC²

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Solution

• [ Pythagoras theorem ]

→ In a right angled triangle, square of hypotenuse is equal to the sum of the square of other two sides.

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★ In right angled isosceles triangle ABC,

$\tt\longmapsto{AB^2 = AC^2 + BC^2}$

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$\tt\longmapsto{AB^2 = AC^2 + AC^2}$ ${\bf{\bigg\lgroup{Given}{\bigg\rgroup}}}$

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$\bf\longmapsto{AB^2 = 2AC^2}$

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$\large{\boxed{\boxed{\sf{Hence\: proved}}}}$

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