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Given two types of geometries are analytic geometry and Euclidean geometry.

Consider analytic geometry.

Analytic geometry, also called coordinate geometry, mathematical subject in which algebraic symbolism and methods are used to represent and solve problems in geometry.

Consider Euclidean geometry.

Euclidean geometry is the study of flat spaces. It describes the relations ship between lines and planes without any numerical measurement.

Answer:

We prefer Analytical geometry because it gives the position of the points in cartesian coordinates. It helps to find the measure of length between points.

Analytical geometry is easier to extend beyond two dimensions.

Consider the triangle, we need to find the angle of the triangle.

According to Euclidean geometry, we can draw triangles by using axioms, but it is difficult to find angles.

According to Analytical geometry, we can find angles by using the coordinates values by using the distance formula and sine law.

Hence I approach Analytical geometry.

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