Mathematically prove that a Beta prior distribution is conjugate to a Geometric likelihood function

I have to prove with a simple example and a plot how prior beta distribution is conjugate to the geometric likelihood function. I know the basic definition as

'In Bayesian probability theory, a class of distribution of prior distribution θ is said to be the conjugate to a class of likelihood function $f(x|\theta )$ if the resulting posterior distribution is of the same class as of $f(\theta )$.'

But I don't know how to prove it mathematically.

I have to prove with a simple example and a plot how prior beta distribution is conjugate to the geometric likelihood function. I know the basic definition as

'In Bayesian probability theory, a class of distribution of prior distribution θ is said to be the conjugate to a class of likelihood function $f(x|\theta )$ if the resulting posterior distribution is of the same class as of $f(\theta )$.'

But I don't know how to prove it mathematically.