Question

Regular octahedron has 8 congruent faces which are isosceles triangles.
A. True
B. False

Answer 1

Hint: In the above given question, we are given a solid shape that is a regular octahedron. A statement is given about a regular octahedron, stating that a regular octahedron has 8 congruent faces which are isosceles triangles. We have to determine if the given statement about a regular octahedron is true or false. In order to approach the solution, we have to consider the geometry of a regular octahedron.

Complete answer:
Given that, a solid shape of the regular octahedron.
We have to determine if a regular octahedron has isosceles triangular faces or not.
Now, we know that an octahedron is a solid shaped polyhedron which has 8 faces and 12 sides i.e. edges. It has 6 pointy vertices.
A regular octahedron has all of its edges equal to each other.
As a result, all of its faces are also equal i.e. congruent to one another.
A regular octahedron is obtained by joining two congruent square pyramids such that the vertices of the two square pyramids coincide. It is a square bi-pyramid in any of three orthogonal orientations.
The shape of a regular octahedron can be drawn as the figure given below.

That is the geometrical shape of a regular octahedron.
Now, in an isosceles triangle, any two sides are equal.
But here we can see that the regular octahedron is made up of 8 triangles, but since all of its sides are equal, that means the three sides of all the 8 triangles are equal to each other.
Therefore, a regular octahedron has 8 congruent triangular faces which are equilateral triangles.
Hence, the given statement is false.

Therefore, the correct option is B

Note: The shape of a regular octahedron looks similar to the shape of a diamond. However, other example of a regular octahedron is the chemical compound molybdenum hexacarbonyl, \[Mo{\left( {CO} \right)_6}\] . The similar polyhedron to a regular octahedron is the regular tetrahedron which looks like exactly half the shape of a regular octahedron as it is a square pyramid itself.