Question

Assertion : ABC is an isosceles triangle right angled at C then AB2 = 2AC2. Reason: If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.​

Answer 1

Answer:

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Answer 2

Given: ABC is an isosceles triangle right angled at C then AB2 = 2AC2. Reason: If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Lets check assertion

ΔABC is an isosceles triangle and ∠C=90°

∴by applying  Pythagoras theorem

$(A B)^{2}=(A C)^{2}+(B C)^{2}$

$\text { Now, } \because \triangle A B C \text { is isosceles, } \quad A C=B C]$

$o^{\circ} \cdot(A B)^{2}=(A C)^{2}+(A C)^{2}$

$(A B)^{2}=2(A C)^{2}$

$\text { Hence, A\overline{ssertion is cornect. }}$Hence , assertion is correct.