Triangles · Class 10 · CBSE Mathematics

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

Practice question from Triangles (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

easy · Subjective · Q-F66502

ABC is an isosceles triangle right-angled at C. Prove that $AB^2 = 2AC^2$ .

Answer: In triangle ABC, since it is right-angled at C, by Pythagoras theorem we have

AB^2 = AC^2 + BC^2

. Given that triangle ABC is an isosceles triangle, its two perpendicular sides are equal, so

AC = BC

. Substituting

BC = AC

into the equation gives

AB^2 = AC^2 + AC^2

, which simplifies to

AB^2 = 2AC^2

Solution

Apply Pythagoras theorem in $\triangle ABC$ where $\angle C = 90^\circ$ , giving $AB^2 = AC^2 + BC^2$ . Substitute $BC = AC$ (since it's isosceles) to get $AB^2 = 2AC^2$ .

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