Q6 of 42 Page 220

ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2.

Since the triangle is right angled at C


∴ the side AB is hypotenuse.


⇒ Let the base of the triangle be AC and the altitude be BC.


⇒ Applying the Pythagorean theorem


⇒ HYP2 = Base2 + Alt2


⇒ AB2 = AC2 + BC2


Since the triangle is isosceles triangle two of the sides shall be equal


∴ AC = BC


Thus AB2 = AC2 + BC2


AB2 = 2AC2


Hence, proved


More from this chapter

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