Question

ABC is an isosceles triangle. if angle B =90°, then prove that AC^2=2BC^2

Answer 1

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Answer 2

Answer:

∆ ABC is an isosceles right angled triangle with right angle at B, then AC² = 2 BC² .

Step-by-step explanation:

• Isosceles right angled triangle is a triangle with one angle equal to 90⁰ and two sides containing the right angled are equal.
• If the right angle is at B, then side AB = BC.

To prove:

• AC² = 2 BC².

Proof:

• Let, ∆ ABC be an isosceles right angled triangle with right angle at B and having two equal AB = BC = a units.
• Since, ∆ ABC is a right angled triangle, using Pythagoras theorem, we get :

${AC}^{2} = {AB}^{2} + {BC}^{2} \\ {AC}^{2} = {a}^{2} + {a}^{2} \\ = 2 {a}^{2} \\since \: BC = \: a \: \: \: \: we \: get \\ \\ {AC}^{2} = 2{BC}^{2}$

• Hence proved.