Question

Require good & detailed answers .

In an Isosceles triangle , AC = BC, if AB² = 2AC²

What is the measure of angle C.

:)

Answer 1

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 buddy!

Answer 2

Hey dear here is your answer!!!!!

___________________________

We have been given an isosceles triangle ABC where, AC = BC.

We have been given AB² = 2AC².

We can re - write it as :-

AB² = AC² + AC²

AB² = AC² + BC²                               ....(AC = BC)

This equation shows the relation between the sides of a right - angled triangle through Pythagoras Theorem.

A Pythagoras Theorem looks in the form of Hypotenuse² = Base² + Perpendicular²

Here, AB would be the hypotenuse and AC & BC would serve as base and perpendicular.

Since, AB is the hypotenuse.

The Δ ABC is right-angled at ∠C.    

...(Angle opposite to Hypotenuse)

Therefore, ∠C = 90°                             ...(Right Angle)

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❣️⭐ Hope it helps you dear...⭐⭐❣️❣️