Question

In an isosceles triangle abc, if ac=bc and ab^2 = 2 ac^2, then angle c=

Answer 1

$\sf\huge\underline{\underline{Solution:}}$

▪Given that,

• AC = BC

• AB² = 2AC²

▪To find,

• Angle C

______________________________________

AB² = AC² + AC²

We are given AC = BC,

Now,

AB² = AC² + BC²

It is Pythagoras equation ( As it involves three sides of the triangle which is Hypotenuse² = side² + side² )

So from the above,

AB is the hypotenuse.

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

So, The angle C measures 90°

Answer 2

▪Given that,

AC = BC

AB² = 2AC²

▪To find,

Angle C

AB² = AC² + AC²

We are given AC = BC,

Now,

AB² = AC² + BC²

It is Pythagoras equation ( As it involves three sides of the triangle which is Hypotenuse² = side² + side² )

So from the above,

AB is the hypotenuse.

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

So, The angle C measures 90°