Question

How many congruent faces does a cube have?

Answer 1

Hint: Try to recall the different examples of things which are cubical in shape and we use in our day today life, for example: Rubik’s cube, boxes etc. Also, remember that the cube has six faces and 12 edges, all the six faces are square with equal side lengths.

Complete step-by-step answer:
We know that two geometrical shapes are called congruent when they have the same shape and size. Congruency in shape and size in two dimensions is measured with at most two parameters : length and measure of angles. The faces of a cube are quadrilaterals that will be congruent if and only if their respective sides and angles will be equal.
Let us start the solution by knowing the structural property of a cube and drawing a representative diagram of it. In mathematics, the word cube refers to a polyhedron which consists of squares as its faces.
Now let us draw a diagram for better visualisation.

Now, we know that each edge of a cube has equal sides and all the faces are square. So, we can say that each face has the same side length and as all are squares, so same interior angles as well, i.e. $90^0$. So, we can conclude that all the faces of a cube are congruent and a cube has a total of 6 faces.
So, we can conclude that a cube has a total of 6 congruent faces.

Note: It is important that you remember all the properties and specifications related to different 3-dimensional figures like cube, cuboid, prism, pyramid etc. It is also important that you know that cuboid and cubes are a type of prisms with base as a rectangle and square, respectively.