Question

 The Euclidean geometry is valid only for figures in the plane.
A.True
B.False
C.Ambiguous
D.Data insufficient

Answer 1

Hint: We are given a statement about the Euclidean geometry. As we know that Euclidean geometry is used in understanding the geometry of flat or two-dimensional spaces.
Euclidean geometry is useful in many fields. We have to determine whether the given statement is true or false. So, we will check whether the statement is valid or not and will show through some figures.

Complete step by step answer:

We are given a statement that “the Euclidean geometry is valid only for figures in the plane”. We have to check whether the statement is true or false.
As we know about the Euclidean geometry that it is applicable for the geometry of flat or two-dimensional spaces and non-Euclidean geometry studies about the curved rather than flat surfaces.
We will draw a figure which shows the Euclidean geometry,

The given statement is true as if we follow Einstein’s theory of general relativity, physical space itself is not Euclidean. Euclidean space is a good approximation for it where the gravitational field is weak. So, in space or in multidimensional space the Euclidean theorems or axioms are not valid as the Euclidean geometry is only valid for the 2-dimensional spaces.
Hence, option A is correct.

Note: We just have to follow the basic definition of Euclidean geometry and as the statement also says that the Euclidean geometry is valid only for planes which refer to the flat surfaces or two-dimensional spaces. We can draw figures to show how the Euclidean geometry looks like.