Question

in an isosceles triangle ABC if AC is equal to BC and AB square is equal to 2 AC square then angle C is equal to

Answer 1

given that:
AC=BC
AB=2AC²
⇒AB=AC²+BC²

∵we know that if the sum of squares of two sides of a triangle is equal to the third side, then the triangle is a right angle triangle

∴∠C=90°                               (Ans.)

Answer 2

Hello there!

Thanks for the question.

So, It's given that

AC = BC

and also ,

AB² = 2AC²

From this,

You can write

AB² = AC² + AC²

This looks like Pythagoras theorem. But yeah, Comparison of just two sides won't make it complete. That's why We are given AC = BC,

Now our equation looks,

AB² = AC² + BC²

This is now looking like Pythagoras equation ( As it involves three sides of the given triangle) which is Hypotenuse² = side² + side²

So from the above relationship,

You can say AB is the hypotenuse.

Since, AB is the hypotenuse, C is right angled.

Simple, So The angle C measures 90°

Hope you are helped !