Question

ABC is an isosceles triangle WITH AC=BC. If AB^=2AC^ prove that ABC is a right triangle

Answer 1

Answer:

Very Easy

Step-by-step explanation:

AB² = 2AC²

⇒ AB² = AC² + AC²

⇒ AB² = AC² + BC²        [∵  AC=BC]      ---------- (1)

∴ Δ is a right angled triangle right angled at C because equation(1) follows pythagoras theorem .

Answer 2

Correct question:-

ABC is an isosceles triangle with AC=BC. If AB^2=2AC^2 prove that ABC is a right triangle.

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Given that:-

• ABC is an isosceles triangle .

• AC = BC

• AB^2 = 2AC^2

To prove:-

• ABC is a right triangle

_____________________________

Proof

AB² = 2AC² - (Given)

AB² = AC² + AC²

AB² = AC² + BC² - (As AC = BC)

Thus, AB is the largest side i.e the (Hypotenuse).

By the Converse of Pythagoras theorem,

∠C = 90°

Hence its a right angle triangle.

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