Question

If the equals are added to equals then, the wholes are ____________
A). Unequal
B). Equal
C). Sometimes equal sometimes unequal
D). Nearest to each other

Answer 1

Hint: There are three types of geometry (1) Euclidean, (2) Spherical, and (3) Hyperbolic. This question is from Euclidean geometry. Euclid has developed the fundamentals of geometry like shapes and figures and also stated five axioms. Before we get to solve this question, we need to know about Euclid’s axioms. There are five axioms, the first main axiom is, “If the equals are added to the equals, then the wholes are also equal”.

Complete step-by-step solution:
In Euclidean geometry theorems are derived as a simple axiom and they do not have any proof. This is something that deals with lines, triangles, points, and shapes.
The given question is, If the equals are added to equals then, the wholes are __________.
As we know, this is one of the axioms that are stated by Euclidean for geometry.
Let us state that axiom once again, “If the equals are added to the equals, then the wholes are also equal”. By reading the statement itself we got the answer that is, If the equals are added to equals then, the wholes are equal.
Now let us see which option is the correct option.
Option (a) Unequal, this option cannot be the right option because the axiom tells us that the wholes are equal so, it cannot be unequal.
Option (b) Equal, is the correct option because from the axiom we got that wholes are equal.
Option (c) Sometimes equal sometimes unequal, this cannot be the right answer because by the axiom the whole as to be equal not sometimes equal or sometimes unequal.
Option (d) Nearest to each other, this option cannot be the right answer since, from the axiom we got that the wholes are equal. Nearest to each other doesn’t mean that they are equal.
Hence, option (b) Equal is the correct answer.

Note: Geometry other than Euclidean is called non-Euclidean geometry. Euclidean geometry is a study of objects or images having flat surfaces, objects other than these will come under non-Euclidean geometry. One of the real-life examples of Euclidean geometry is architecture, where they use Euclidean geometry to develop the structure of buildings.