why does a need goemetry for goemetry and algebra to study goemetry?

Answer 1

I'm not entirely certain what you mean: Are you meaning to say "Why do you need algebra for geometry and geometry for algebra?"

If that's the question, then the idea is that the two subjects share fundamental links, so it's reasonable to learn them more or less concurrently.

Answer 2

You need algebra to study geometry to solve algebraic equations that come up in geometry.

Example the Pythagorean Theorem for a right triangle:

a² + b² = c²
.

Answer 3

You seem rather to be needing some grammar, and bad.
It is "geometry"
Regards
Tonio